20b_01w_1e

# 20b_01w_1e - but it should NOT contain trig functions 3(12...

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Math 20B First Exam 4:40 PM January 29, 2001 Please put your name, ID number, and section number (or time) on your blue book. The exam is CLOSED BOOK. Calculators are NOT allowed. You must show your work to receive credit. 1. (48 pts.) Evaluate the following. Remember to show your work! (a) lim x 0 cos x - 1 e x - 1 . (b) F 0 ( x ) given that F ( x )= Z 2 x cos( t 2 ) dt. (c) Z e t 1+ e t dt. (d) Z 2 0 | x - 1 | dx. 2. (20 pts.) (a) Verify that ln | sin u | is an antiderivative of cot u . (b) Compute Z π/ 2 π/ 4 cot xdx . Your ﬁnal answer may contain logarithms,
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Unformatted text preview: but it should NOT contain trig functions. 3. (12 pts.) Verify the inequality Z 1 p 2 + x 2 dx 3 without evaluating the integral. 4. (a) (15 pts.) Given the table of information below, use a linear approximation to estimate g (16). x 5 10 15 g ( x ) 0 20 35 45 (b) (5 pts.) Do you think your prediction is an overestimate or underestimate? Why? You must give a reason to receive credit. END OF EXAM...
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