Ap calculus ab
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AP Calculus AB. Day 13 Section 3.9. Linear Approximation. Non-calculator application of the tangent line. Used to estimate values of f(x) at ‘difficult’ x-values. (ex: 1.03, 2.99, 7.01) Steps: a.Find the equation of the tangent line to f(x) at an ‘easy’ value nearby.

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AP Calculus AB

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Ap calculus ab

AP Calculus AB

Day 13

Section 3.9

Perkins


Linear approximation

Linear Approximation

Non-calculator application of the tangent line.

Used to estimate values of f(x) at ‘difficult’ x-values.

(ex: 1.03, 2.99, 7.01)

Steps:

a.Find the equation of the tangent line to f(x) at an ‘easy’ value nearby.

b.Plug the ‘difficult’ x-value in to get a reasonable estimate of what the actual y-value will be.


Ap calculus ab

1. Find the equation of the tangent line to f(x) at x = 1.


Ap calculus ab

2. Use the equation of the tangent line to f(x) at x = 1 to estimate f(1.01).

This estimate will be accurate as long as the x-value is very close to the point of tangency.


Ap calculus ab1

AP Calculus AB

Day 13

Section 3.9

Perkins


Linear approximation1

Linear Approximation


Ap calculus ab

1. Find the equation of the tangent line to f(x) at x = 1.


Ap calculus ab

2. Use the equation of the tangent line to f(x) at x = 1 to estimate f(1.01).


Ap calculus ab

Finding Differentials

To estimate a y-value using a differential:

1. Find a y-value at a nearby x-value.

2. Add the value of your differential.

Differential

Change in y.

Change in x.

Slope of tangent line at a given x.

3. Estimate f(0.03) without your calculator.

4. Estimate f(8.96) without your calculator.


Ap calculus ab

Finding Differentials

3. Estimate f(0.03) without your calculator.

4. Estimate f(8.96) without your calculator.


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