Warm up december 19 2012
This presentation is the property of its rightful owner.
Sponsored Links
1 / 23

Warm-Up: December 19, 2012 PowerPoint PPT Presentation


  • 34 Views
  • Uploaded on
  • Presentation posted in: General

Warm-Up: December 19, 2012.

Download Presentation

Warm-Up: December 19, 2012

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


Warm up december 19 2012

Warm-Up: December 19, 2012

  • 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.


Warm up december 19 20121

Warm-Up: December 19, 2012

  • Rectangular pool

  • Area = 1800 sqft

  • 5 ft deck on sides

  • 10 ft deck on ends

  • Minimize property area


Homework questions

Homework Questions?


4 1 4 3 questions

4.1-4.3 Questions?


4 1 4 3 quiz

4.1-4.3 Quiz

  • 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


Warm up december 20 2012

Warm-Up: December 20, 2012

  • Write the equation of the line tangent to


Homework questions1

Homework Questions?


Linearization and newton s method

Linearization and Newton’s Method

Section 4.5


Warm up expanded

Warm-Up, Expanded

  • Graph each of the following on your graphing calculator:

  • Start with a standard window

  • Zoom in at the origin repeatedly and observe what occurs


Linearization

Linearization

  • 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)


Example 1 page 229 4

Example 1 – page 229 #4

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

  • How accurate is the approximation


Example 2 page 229 12

Example 2 – page 229 #12

  • 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.


Assignment

Assignment

  • 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)


Warm up december 21 2012

Warm-Up: December 21, 2012

  • Without a calculator, estimate


Homework questions2

Homework Questions?


Newton s method

Newton’s Method

  • Uses linearizations to find the zeros of a function.

  • Process repeats until the answers converge.


Newton s method1

Newton’s Method

  • 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


Example 3

Example 3

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


Differentials

Differentials

  • Differentials are like very small deltas

  • Finding a differential is similar to finding a derivative


Example 4

Example 4

  • Find the differential dy.

  • Evaluate dy at x=2, dx=0.1


Example 5

Example 5

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


Assignment1

Assignment

  • 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)


  • Login