1 / 23

# Warm-Up: December 19, 2012 - PowerPoint PPT Presentation

Warm-Up: December 19, 2012.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Warm-Up: December 19, 2012' - elmo-osborne

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

• A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5-foot wide decks along either side and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions.

• Rectangular pool

• Area = 1800 sqft

• 5 ft deck on sides

• 10 ft deck on ends

• Minimize property area

• Clear everything off of your desk except pencil and eraser.

• NO CALCULATOR!

• 20 minute time limit

• You must remain silent until all quizzes have been turned in.

• If you finish early, reread Section 4.5

• Write the equation of the line tangent to

### Linearization and Newton’s Method

Section 4.5

• Graph each of the following on your graphing calculator:

• Zoom in at the origin repeatedly and observe what occurs

• If f is differentiable at x=a, then f is locally linear.

• Zooming in very close, f looks like a straight line.

• The linearization of f at a is:

• The approximation f(x)≈L(x) is the standard linear approximation of f at a.

• (Related to Taylor Series – Calculus BC topic)

• Find the linearization L(x) of f(x) at x=a

• How accurate is the approximation

• Choose a linearization with center not at x=a but at a nearby value at which the function and its derivative are easy to evaluate. State the linearization and the center.

• Read Section 4.5 (pages 220-228)

• Page 229 Exercises #1-13 odd

• Page 229 Exercises #15-35 odd

• Read Section 4.6 (pages 232-236)

• Without a calculator, estimate

• Uses linearizations to find the zeros of a function.

• Process repeats until the answers converge.

• Step 1: Guess an approximate root/zero/x-intercept, x1

• Step 2: Use the first approximation to get a second approximation

• Use the second approximation to get a third, the third to get a fourth, and so on

• Use Newton’s method to estimate all real solutions of the equation. Make your answers accurate to 6 decimal places.

• Differentials are like very small deltas

• Finding a differential is similar to finding a derivative

• Find the differential dy.

• Evaluate dy at x=2, dx=0.1

• Write a differential formula that estimates the change in surface area of a sphere when the radius changes from a to a+dr.

• Read Section 4.5 (pages 220-228)

• Page 229 Exercises #1-13 odd

• Page 229 Exercises #15-35 odd

• Read Section 4.6 (pages 232-236)