'Tangent line approximation' presentation slideshows

DIFFERENTIATION RULES

3. DIFFERENTIATION RULES. DIFFERENTIATION RULES. We have seen that a curve lies very close to its tangent line near the point of tangency. DIFFERENTIATION RULES.

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DERIVATIVES

3. DERIVATIVES. DERIVATIVES. We have seen that a curve lies very close to its tangent line near the point of tangency. DERIVATIVES. In fact, by zooming in toward a point on the graph of a differentiable function, we noticed that the graph looks more and more like its tangent line.

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DIFFERENTIATION RULES

3. DIFFERENTIATION RULES. DIFFERENTIATION RULES. We have seen that a curve lies very close to its tangent line near the point of tangency. DIFFERENTIATION RULES.

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DERIVATIVES

3. DERIVATIVES. DERIVATIVES. We have seen that a curve lies very close to its tangent line near the point of tangency. DERIVATIVES. In fact, by zooming in toward a point on the graph of a differentiable function, we noticed that the graph looks more and more like its tangent line.

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DERIVATIVES

3. DERIVATIVES. DERIVATIVES. 3.9 Linear Approximations and Differentials. In this section, we will learn about: Linear approximations and differentials and their applications. LINEAR APPROXIMATIONS. The idea is that we use the tangent line at

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DERIVATIVES

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Section 4.7

Section 4.7. Optimization Problems. Example 8. A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. Section 4.8. Differentials.

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The Teaching of Mathematics: What Changes are on the Horizon?

The Teaching of Mathematics: What Changes are on the Horizon?. Deborah Hughes Hallett University of Arizona Harvard University. Why Change? A US-European Perspective. Role of Mathematics and Statistics is Changing: More fields require more mathematics (eg bioinformatics, finance)

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MATH 1910 Chapter 3 Section 9 Differentials

MATH 1910 Chapter 3 Section 9 Differentials. Objectives. Understand the concept of a tangent line approximation. Compare the value of the differential, dy , with the actual change in y , ? y . Estimate a propagated error using a differential.

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Calculus: Hughs-Hallett Chap 4

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Chapter 2 Calculus: Hughes-Hallett

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Linear Approximation and Differentials

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2.9

Linear Approximation. 2.9. We have seen that a curve lies very close to its tangent line near the point of tangency. In fact, by zooming in toward a point on the graph of a differentiable function, we noticed that the graph looks more and more like its tangent line.

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What is y=L(x) ?

What is y=L(x) ?. The tangent line is considered as an approximation of the curve y=f(x). The tangent line is considered as an approximation of the curve y=f(x). is called the linear approximation or tangent line approximation. is called the linearization of f at a. Example: F091.

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Problem 8.2.6 from textbook

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Using a tangent line approximation of the function , find an approximate value for

Using a tangent line approximation of the function , find an approximate value for. Tangent line. (9,3). Using a tangent line approximation of the function , find an approximate value for. The first step is to find some exact value of the function near x=11.

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Section 3.9 - Differentials

Section 3.9 - Differentials. Tangent Line Approximations A tangent line approximation is a process that involves using the tangent line to approximate a value. Newton used this method to approximate zeros of functions. Another use of this method is to approximate the value of a function.

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3.7 Differentials p. 267

3.7 Differentials p. 267. Tangent lines can be used to approximate function values. Tangent line approximation. *also called a linear approximation or the linearization of a function. *can yield excellent approximations of f if sufficiently close to c.

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