- 121 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' AP Calculus AB' - karena

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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.

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.

Linear Approximation estimate f(1.01).

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

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

Finding Differentials estimate f(1.01).

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.

Finding Differentials estimate f(1.01).

3. Estimate f(0.03) without your calculator.

4. Estimate f(8.96) without your calculator.

Download Presentation

Connecting to Server..