# Test 1b - 2 x 2-x-2 x 2-3 x + 2 b ) lim x 1 x 2 + 25 x-5 c...

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Test I for Calculus I, Math 1501E1, September 10, 2002 Name: This test is to be taken without calculators and notes of any sorts. The allowed time is 50 minutes. Write answers in boxes where provided. Provide exact answers; not decimal approximations! For example, if you mean 2 do not write 1 . 414 . . . .

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I: (25 points, no partial credit) a) For some function f ( x ) you know that | f (2 + h ) - f (2) | ≤ 7 | h | 3 . Find δ > 0 so that | f (2 + h ) - f (2) | < ε whenver | h | < δ . b) True or false 0 < a < 1 a > a 0 < a < 1 a 2 < a c) Find all x for which x 2 + 3 x + 2 > 0 d) Find the linear function ( x ) whose slope is - 2 and has the point (1 , 2) on its graph. e) Find the linear function ( x ) that has the points (1 , 2) and (2 , 3) on its graph.
II: (25 points) Which of the following limits exist? If compute them if they exist. Otherwise, explain why they do not exist. a ) lim x

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Unformatted text preview: 2 x 2-x-2 x 2-3 x + 2 b ) lim x 1 x 2 + 25 x-5 c ) lim x 1-cos( x 1+ x ) x 2 d ) lim x 1 p | x-1 | + 1-1 | x-1 | e ) lim x | tan( x ) | x III: (25 points) Given the function f ( x ) = 2 1 + x 2 . a) Find all values for x that satisfy | f ( x )-1 | < 1 b) Find g ( h ) so that | f (1 + h )-f (1) | = g ( h ) | h | c) For > 0, nd > 0 so that | h | < | f (1 + h )-f (1) | < IV: (25 points) Show, using Mathematical Induction, that for x 6 = 1 (1 + x )(1 + x 2 )(1 + x 4 ) (1 + x 2 n ) = 1-x 2 n +1 1-x . Fill in the following steps: a) Check the statement for n = 0 and n = 1. b) Write down the Induction Assumption: c) Carry out the Induction Step:...
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## This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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Test 1b - 2 x 2-x-2 x 2-3 x + 2 b ) lim x 1 x 2 + 25 x-5 c...

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