2002 Fall - Fall_2002 math125

2002 Fall - Fall_2002 math125 - MATH 125 FINAL EXAM...

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MATH 125 FINAL EXAM December 17, 2002 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 . [5 points each] Evaluate the limits, if they exist. (a) lim x 2 x 2 + 2 x - 8 x - 2 (b) lim x 2 - x 2 + 2 x - 5 x - 2 (c) lim x 0 sin x tan x 2 x 2 (d) lim x →∞ ( x 2 + x - x ) 2 . [6 points each] Find the derivatives of the following functions. (a) f ( x ) = e x +7 , x > 0. (b) f ( x ) = ln ( x (2 + sin x )), x > 0. (c) f ( x ) = Z x 2 2 cos u 2 du (d) f ( x ) = (1 + x 2 ) x .
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3 . [6 points each] Evaluate the following integrals, giving your answers in as simple a form as possible. (a) Z x 2 + 2 x x dx (b) Z ln 18 0 xe x 2 dx (c) Z x 1 + x dx (d) Z π/ 2 0 cos x sin x dx 4 . [30 points] Sketch the graph of the function f ( x ) = x ( x + 3) 2 using the axes provided and fill in the required information below. If none, write NONE.
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