hw8-29 - 3. The graph of a function f ( x ) is shown below....

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Math 170-010 Homework 8/29 Fall 2011 Goals: Learn vocabulary and notation of limits. Use a table of values to estimate a limit. Use algebraic techniques to compute limits. Exercises: 1. Consider the function m ( x ) = 5 - 169 - x 2 12 - x (a) Complete the table of values x 11.9 11.99 11.999 12 12.001 12.01 12.1 m [HINT: You already did some of this in Hw 8/26.] (b) Use it to estimate lim x 12 m ( x ) 2. Consider the function m ( x ) = 1 /x - 1 / 3 x - 3 (a) Complete the table of values x 2.9 2.99 2.999 3 3.001 3.01 3.1 m [HINT: You already did some of this in Hw 8/26.] (b) Use it to estimate lim x 3 m ( x ) 3. Consider the function f ( t ) = 320 e - 3 . 1 t - 320 e - 3 . 1 t - 1 (a) Complete the table of values t 0.98 0.99 1.00 1.01 1.02 f (b) Use it to estimate lim t 1 f ( t ) 4. For the function f ( t ) = 2 sin( π ( t - 0 . 5)) t - 0 . 5 , make an appropriate table of values and use it to estimate lim t 0 . 5 f ( t ) 5. From the Online Textbook, Section 2.3, Problems 1, 2, 3, 4, 5 and 20. 1
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Challenge Problems: 1. Solve Problem 2 above using exact algebraic methods. 2. Solve Problem 1 above using exact algebraic methods.
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Unformatted text preview: 3. The graph of a function f ( x ) is shown below. DeFne a new function m ( x ) = f ( x )-f (20) x-20 Create an appropriate table of values for m ( x ) and use it to estimate lim x 20 m ( x ). 2 Hints and Answers Exercises: 1. x 11.9 11.99 11.999 12 12.001 12.01 12.1 m-2 . 34-2 . 39-2 . 40 DNE-2 . 40-2 . 41-2 . 47 lim x 12 m ( x ) -2 . 4 2. x 2.9 2.99 2.999 3 3.001 3.01 3.1 m-. 1149-. 1115-. 1111 DNE-. 1111-. 1107-. 1075 lim x 3 m ( x ) -. 1111 3. t 0.98 0.99 1.00 1.01 1.02 f-46 . 1-45 . 4 DNE-44 .-43 . 3 lim t 1 f ( t ) -44 . 7 4. t 0.48 0.49 0.50 0.51 0.52 f 6 . 279 6 . 282 DNE 6 . 282 6 . 279 lim t . 5 f ( t ) 6 . 282 5. All answers available in Appedix A of the Online Textbook. Challenges: 1.-12 5 2.-1 9 3. Approx-. 29. 3...
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This note was uploaded on 10/11/2011 for the course MATH 170 taught by Professor Staff during the Fall '08 term at Boise State.

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hw8-29 - 3. The graph of a function f ( x ) is shown below....

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