Created by Sal Khan. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 1 Integrals review. actually an ellipse is determine by its foci. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Interpreting direction of motion from position-time graph. For example, the domain of f (x)=x² is all real numbers, and the domain of g (x)=1/x is all real numbers except for x=0. Beyond that, the tricky part is wrestling with bounds, and the nastiness of actually solving the integrals that you get. Learn about the concept of center of mass and its real-world applications. The denominator of a rational function can't tell you about the horizontal asymptote, but it CAN tell you about possible vertical asymptotes. If you input 0 through 4 into the function, multiplying every outcome by whatever interval you're testing with, say 0. Unit 6 Integrals. Understand how objects with uniform density have their center of mass at the geometric center, and how this changes with non-uniform density. Unit 5 System of equations. The outer radius is defined in a later video as the distance from the axis of rotation to the outer function. First lets establish a closed interval where the function is continuous. What we're doing is for each x, we're finding a little dx around it-- so this right over here is a little dx. This is the easier method. Test your knowledge of the skills in this course. Our interactive practice problems, articles, and videos help studen. Unit 3 Derivatives: chain rule and other advanced topics. AP®︎/College Calculus BC 12 units · 205 skills. In this case, y is treated as a. The critical points of a function f are the x -values, within the domain of f for. Courses on Khan Academy are always 100% free. Think about the limit of. Unit 2 Differentiation: definition and basic derivative rules. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. · Differential Calculus cuts something into small pieces to find how it changes. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Watch the next lesson: https://www. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 3 Derivatives: chain rule and other advanced topics. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. For example, if ultimately you plan to plug in y=5, when you see an expression. Unit 3 Derivatives: chain rule and other advanced topics. Unit 1 Limits and continuity. In multivariable calculus—and beyond—the word operator comes up a lot. Thus, if you are given x (t) and y (t) (we say "parametric" equations for x and y), then we can write this as: Basically, we have "divided" everything inside the radical by dt², and so we then multiply on the outside of the radical simply by dt. 1/100² = 1/10000 etc. Unit 5 Analyzing functions. Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Unit 3 Derivatives: chain rule and other advanced topics. time, or by using kinematic formulas if the. Course challenge. You end up with, well, a field of vectors sitting at various points in two-dimensional space. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. A vector-valued function is a function whose value is a vector, like velocity or acceleration (both of which are functions of time). d A = r d r d θ. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Think about the limit of. Find two numbers whose products is -16 and the sum of whose squares is a minimum. When a person opens a door, they push on the side of the door farthest from the hinges. If the ratio near infinity is less than 1, then we know for certain that each term is becoming less and less and the series will converge. Taking the derivative at a single point, which is done in the first problem, is a different matter entirely. Solving equations & inequalities: Algebra 1. So what we're doing is we're multiplying this width times this height right over here. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. So if f and g are defined, L'Hôpital would be applicable only if the value of both f and g is 0. Functions assign outputs to inputs. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. About Khan Academy: Khan Academy is a nonprofit with a. Unit 4 Applications. Start Course challenge Unit 1: Limits and continuity 0/3500 Mastery points Limits intro Estimating limits from graphs Estimating limits from tables Formal definition of limits (epsilon-delta) Properties of limits Limits by direct substitution Limits using algebraic manipulation Strategy in finding limits. College Board has no control over their content and cannot vouch for accuracy. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. This is done using the chain rule, and viewing y as an implicit function of x. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. So y = x^2 -2 shifts the whole function down 2 units, and y ≥ -2. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. 7M views 12 years ago Precalculus Courses on Khan Academy are always. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Calculus 1 Calculus 2 Multivariable calculus Differential equations Linear algebra Early math Counting Addition and subtraction. They will show up all over multivariable calculus, so let's get into it. Unit 1 Limits and continuity. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Remember that the derivative of 2x-3 is 2, thus to take the integral of 1/ (2x-3), we must include a factor of 1/2 outside the integral so that the inside becomes 2/ (2x-3), which has an antiderivative of ln (2x+3). Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. A function is called multivariable if its input is made up of multiple numbers. Sure, it's because of the chain rule. Introduction to Calculus. One way to include negatives is to reflect it across the x axis by adding a negative y = -x^2. By treating the other variable like a constant, the situation seems to simplify to something we can understand in terms of single-variable. The consumer's got $30,000 more in benefit, marginal benefit for them and value for themselves, than they had to pay for it. The fundamental theorem of calculus shows how, in some sense, integration is the opposite of differentiation. In this video, we learn about parametric equations using the example of a car driving off a cliff. Optimization: cost of materials. Optimization: area of triangle & square (Part 1) Optimization: area of triangle & square (Part 2) Optimization problem: extreme normaline to y=x². Material for the base costs $10 per square meter. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ( 13 votes). Beyond that, the tricky part is wrestling with bounds, and the nastiness of actually solving the integrals that you get. Unit 3 Non-right triangles & trigonometry. The Power Rule is for taking the derivatives of polynomials, i. y = -x when x < 0. The length of its base is twice the width. Unit 6 Parametric equations, polar coordinates, and vector-valued functions. Ready to find the perfect math curriculum for your students? 1. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. These courses offer a way to get college credit during high school. The original equation describing movement on a line was. Learn for free. The Fundamental Theorem of Calculus tells us that the derivative of the definite integral from 𝘢 to 𝘹 of ƒ (𝑡)𝘥𝑡 is ƒ (𝘹), provided that ƒ is continuous. For the absolute value function it's defined as: y = x when x >= 0. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. The distance x ( t) between the bottom of the ladder and the wall is increasing at a rate of 3 meters per minute. Subtract the first from the second to obtain 8a+2b=2, or 4a+b=1. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Working with. Proof of infinite geometric series formula. Unit 4 Applications of derivatives. It's taking into account both of these components of the output and both possible inputs. f (x) is continuous for x >= 0 since the function is made by adding multiple square root functions which are also continuous for x>= 0. Finding derivative with fundamental theorem of calculus. This involves replacing the input of one function with the output of another function. ), which are downloaded directly to your iPhone or iPod touch so you don't need Internet access to watch and learn. Unit 6 Integrals. Solving equations & inequalities: Algebra 1. Motion problems: finding the maximum acceleration. , to find an expression for the unit normal vector to this surface, take the following steps: Step 1: Get a (non necessarily unit) normal vector by taking the cross product of both partial derivatives of v → ( t, s) . Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. A graph can help us approximate a limit by allowing us to estimate the finite y. When x changes by an increment Δx, these functions have corresponding changes Δy, Δu, and Δv. Unit 3 Applications of multivariable derivatives. If anyone else wants to add a couple other reasons, they can. Unit 4 Get ready for contextual applications of differentiation. If we divide both sides by x, we get y is equal to negative 16 over x. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Do 4 problems. Unit 6 Integrals. Formal definition of limits Part 3: the definition. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 2 Derivatives: definition and basic rules. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Visualizing vector-valued functions Visualizing multivariable functions (articles) 0/2100 Mastery points. To keep things from getting too messy as we do so,. Through a worked example involving f (x)=√ (x²-1) and g (x)=x/ (1+x), learn about function composition: the process of combining two functions to create a new function. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. So y = x^2 -2 shifts the whole function down 2 units, and y ≥ -2. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. The Power Rule is for taking the derivatives of polynomials, i. AP®︎/College Calculus AB > Contextual applications of differentiation > Approximating values of a function using local linearity and linearization. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 3 Derivatives: chain rule and other advanced topics. When x=3, this expression is 7, since. time, or by using kinematic formulas if the. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. 2^x is an exponential function not a polynomial. AP®︎/College Calculus BC 12 units · 205 skills. Algebra (all content) 20 units · 412 skills. Material for the base costs $10 per square meter. Learn how to find an object’s instantaneous speed or velocity in three ways - by using calculus, by looking at the slope of a given point on a graph of an object’s rate vs. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. It'd be a bit hairy to write that here without good math notation. All the terms in polynomials are raised to integers. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 6 Series. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. About this unit. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Introduction to Calculus. These simple yet powerful ideas play a major role in all of calculus. A vector-valued function is a function whose value is a vector, like velocity or acceleration (both of which are functions of time). In this video, we explore the limit of (x²+x-6)/ (x-2) as x approaches 2. Optimization: box volume (Part 1) Optimization: box volume (Part 2) Optimization: profit. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Functions assign outputs to inputs. Solving equations & inequalities: Algebra 1. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 1 Limits and continuity. However, instead of looking for points where the derivative changes its sign, we are looking for points where the second derivative changes its sign. Unit 3 Laplace transform. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. This means an expression like y^2 just looks like (some constant)^2, which is again a constant. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 8 Applications of integrals. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. You also say it touches the point (3, 3), which tells us 9a+3b+c=3. AP Calculus BC covers Calculus 1 and 2 and is more rigorous. The general form given in both these proof videos, that Green's theorem is dQ/dX- dP/dY assumes that your are moving. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Some relationships cannot be represented by an explicit function. Course challenge. Watch the next lesson: https://www. In this case Sal used a Δx = 1, which is very, very big, and so the approximation is way off, if we had used a smaller Δx then Euler's method would. So if f and g are defined, L'Hôpital would be applicable only if the value of both f and g is 0. Optimization: cost of materials. Calculus 1 8 units · 171 skills. The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Unit 1 Limits and continuity. Consider this problem: A 20 -meter ladder is leaning against a wall. And right at this moment, there is a height of 2. For example, if ultimately you plan to plug in y=5, when you see an expression. Unit 4 Applications. Test your knowledge of the skills in this course. Integration by parts is a method to find integrals of products: ∫ u ( x) v ′ ( x) d x = u ( x) v ( x) − ∫ u ′ ( x) v ( x) d x. These materials enable personalized practice alongside the new Illustrative Mathematics 6th grade curriculum. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. This video introduces limit properties, which are intuitive rules that help simplify limit problems. The AP Calculus courses are a part of a suite of AP courses offered by College Board. All the terms in polynomials are raised to integers. Unit 8 Applications of integrals. The domain of a function is the set of all possible inputs for the function. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 2 Second order linear equations. A function is called multivariable if its input is made up of multiple numbers. So what we're doing is we're multiplying this width times this height right over here. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. In this case, the solution in general may be written as: y^2 + x^2 = c; where c is any constant. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 6 Series. Course: AP®︎/College Calculus AB > Unit 8. Unit 3 Derivatives: chain rule and other advanced topics. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 2 Derivatives: definition and basic rules. We can re-use the axes/dimensions we already have to draw these vectors at the location of each input. You end up with, well, a field of vectors sitting at various points in two-dimensional space. jpw mini monitor speakers review, hesperonis ark
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. . Khan academy calculus
Unit 1 Limits and continuity. Unit 4 Integrating multivariable functions. Trapezoidal sums. Solving equations & inequalities: Algebra 1. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. The main properties covered are the sum, difference, product, quotient, and exponent rules. In this case Sal used a Δx = 1, which is very, very big, and so the approximation is way off, if we had used a smaller Δx then Euler's method would. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Test your knowledge of the skills in this course. AP Calculus BC covers Calculus 1 and 2 and is more rigorous. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. The squeeze (or sandwich) theorem states that if f (x)≤g (x)≤h (x) for all numbers, and at some point x=k we have f (k)=h (k), then g (k) must also be equal to them. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 1 Limits and continuity. About this unit. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Optimization: box volume (Part 1) Optimization: box volume (Part 2) Optimization: profit. The chain rule tells us how to find the derivative of a composite function: d d x [ f ( g ( x))] = f ′ ( g ( x)) g ′ ( x) The AP Calculus course doesn't require knowing the proof of this rule, but we believe that as long as a proof is accessible, there's. In short, power series offer a way to calculate the values of functions that transcend addition, subtraction, multiplication, and division -- and they let us do that using only those four operations. That gives us, among other things, a way to program machines to calculate values of functions like sin (x) and sqrt (x). Learn how we define the derivative using limits. In the video, we're looking at the slope/derivative of f (x) at x=5. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. y is negative 16 over x. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. In this case, y is treated as a constant. The length of its base is twice the width. Unit 5 Analyzing functions. Unit 3 Derivatives: chain rule and other advanced topics. There is also integration parts although in that case you would substitute u= G (x) so you can. Method 2: If it is not possible to convert the problem to a ∫u^ (n) du nor to some other standard integral from, then you can expand out the polynomial and integrate each term separately. Description The Chain Rule Khan Academy 6. Learn about the concept of center of mass and its real-world applications. In multivariable calculus—and beyond—the word operator comes up a lot. Differential equations 3 units · 8 skills. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Interpreting direction of motion from velocity-time graph. What we're doing is for each x, we're finding a little dx around it-- so this right over here is a little dx. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 7 Differential equations. Let's explore how to find the derivative of any polynomial using the power rule and additional properties. Khan Academy: Calculus Browse videos, articles, and exercises about calculus. Hippocampus: Calculus A free, core academic website offering rich multimedia content on general education subjects to. Unit 3 Applications of multivariable derivatives. Learn how we define the derivative using limits. Start practicing—and saving your progress—now: https://www. And then that's what we will now square. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Differential and Integral Calculus are two different types of calculus. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Telescoping series is a series where all terms cancel out except for the first and last one. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 2 Derivatives: definition and basic rules. Graphically, the theorem guarantees that. Problem 3. The domain of a function is the set of all possible inputs for the function. Unit 8 Applications of integrals. *Although Khan Academy offers an AP/College Calculus AB course, the AP/College Calc BC has two extra units in addition to the original 10 units available in AP/College Calc AB. To understand what limits are, let's look at an example. Visualizing vector-valued functions Visualizing multivariable functions (articles) 0/2100 Mastery points. Unit 2 Derivatives: definition and basic rules. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Khan Academy offers free online courses, lessons and practice for calculus from Pre-K to college, as well as other math, science, reading and life skills topics. Limits by factoring. Button navigates to signup page. Parametric equations define x and y as functions of a third parameter, t (time). 3M views 10 years ago Antiderivatives and the fundamental theorem of calculus | AP Calculus BC | Khan Academy Courses on Khan Academy. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Unit 4 Integrating multivariable functions. 1/100² = 1/10000 etc. Not really. The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Unit 1 One-dimensional motion. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Material for the sides costs $6 per square meter. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Unit 8 Oscillations and mechanical waves. Maker: Ximarc Studios Inc. In this case, the indeterminate form is equal to 2. Unit 1 Limits and continuity. The Praxis Core Writing test also includes two essay sections. In this case, the indeterminate form is equal to 2. Interpret motion graphs. Differential equations 3 units · 8 skills. Start Course challenge Unit 1: Limits and continuity 0/3500 Mastery points Limits intro Estimating limits from graphs Estimating limits from tables Formal definition of limits (epsilon-delta) Properties of limits Limits by direct substitution Limits using algebraic manipulation Strategy in finding limits. In the video we are told that each cross section (parallel to the 𝑦-axis) of the 3-dimensional object is a square. Unit 5 Green's, Stokes', and the. Unit 3 Applications of multivariable derivatives. But if order matters, then you read the differentials in the denominator from right to. We can re-use the axes/dimensions we already have to draw these vectors at the location of each input. The word Calculus comes from Latin meaning "small stone". Hippocampus: Calculus A free, core academic website offering rich multimedia content on general education subjects to. Problem set 1 will walk you through all the steps of finding the following integral using u -substitution. Khan Academy is a nonprofit with the mission of providing a free, world-class education for. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Course challenge. 2^x is an exponential function not a polynomial. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Then the second partial derivative test goes as follows: If H < 0. In this case, there were two times when the particle was speeding up. Unit 2 Two-dimensional motion. Unit 3 Derivatives: chain rule and other advanced topics. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. See how this can be used to evaluate the derivative of accumulation functions. If we reverse this process on 1/sqrt (a^2-x^2) (find the indefinite integral) we. In this video, we explore the limit of (x²+x-6)/ (x-2) as x approaches 2. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. . jenni rivera sex tape