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Unformatted text preview: MATH 125 FINAL EXAM May 8, 2003 INSTRUCTIONS Answer all questions. You must show your work to obtain full credit. Points may be deducted if you do not justify your final answer. Please indicate clearly whenever you continue your work on the back of the page. Calculators are not allowed. The exam is worth a total of 200 points. 1 . [24 points] In each case, evaluate the limit if it exists, including ±∞ . Be sure to show your work. If no limit exists, explain why. (a) lim x → 3 x 2 4 x + 3 x 2 + 4 x 21 (b) lim x → sin x  x  (c) lim x → 1 √ 4 x √ x + 3 √ x 1 (d) lim x →∞ e 3 x e 4 x e 7 x 2 . [24 points] Find the derivatives of the following functions. (a) f ( x ) = ( x 2 + x 1)sin x 2 . (b) f ( x ) = x 2 x + 3 . (c) f ( x ) = ln ‡ 1 + e x 3 · (d) f ( x ) = Z x 2 dt t 4 + 1 . 3 . [30 points] Evaluate the following integrals. (a) Z 1 (3 x 1) 4 dx (b) Z 3  x 2 1  dx (c) Z cos x (1 + sin x ) 2 dx (d) Z e 2 x √ 1 + e x dx (e) Z 1 √ x ( √ x + 1) dx 4. [16 points] (i) Give the definition of:...
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This note was uploaded on 09/03/2008 for the course MATH 125 taught by Professor Tuffaha during the Spring '07 term at USC.
 Spring '07
 Tuffaha
 Math, Calculus

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