ma165-practice-finasecondrevision

ma165-practice-finasecondrevision - MA 165 FINAL EXAM...

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MA 165 FINAL EXAM PRACTICE PROBLEMS 1. lim x 1 x 2 - 1 x 2 - x =A . - 1B . 0C . 1D . 2E .D o e s n o t e x i s t 2. If y =( x 2 +1)tan x ,then dy dx . 2 x tan x +( x 2 +1)sec 2 x B. 2 x sec 2 x C. 2 x tan x x 2 x D. 2 x tan x +2 x sec 2 x E. 2 x tan x 3. If h ( x )= ± x 2 + a, for x< - 1 x 3 - 8f o r x ≥- 1 determine all values of a so that h is continuous for all values of x . A. a = - . a = - 8C . a = - 9D . a = - 10 E. There are no values of a . 4. Evaluate lim x 0 + x cos( 1 x ). (Hint: - 1 cos( 1 x ) 1 for all x 6 =0 .) A .0 B .1 C . - . π 2 E. Does not exist 5. If f ( x 1 x +3 , then lim x 1 f ( x ) - f (1) x - 1 . 1 4 B. 1 16 C. - 1 16 D. - 1 4 E. Does not exist 6. The equation x 3 - x - 5 = 0 has one root for x between - 2 and 2. The root is in the interval: A. ( - 2 , - 1) B. ( - 1 , 0) C. (0 , 1) D. (1 , 2) E. ( - 1 , 1) 7. If f ( x 1 - x 1+ x f 0 (1) = A. - . - 1 2 C. 0 D. 1 2 E. 1 8. If y =ln(1 - x 2 )+sin 2 x dy dx . 1 1 - x 2 +cos 2 x B. 1 1 - x 2 +2sin x cos x C. 1 1 - x 2 x D. - 2 x 1 - x 2 2 x E. - 2 x 1 - x 2 x cos x 9. Find f 00 ( x )i f f ( x 1 - x 1+ x A. 4 (1+ x ) 3 B. - 4 (1+ x ) 3 C. - 4 x (1+ x ) 3 + 2 (1+ x ) 2 D. 2(1+ x ) 2 - 2 x (1+ x ) (1+ x ) 4 E. - 1 10. Assume that y is defined implicitly as a differentiable function of x by the equation xy 2 - x 2 + y +5=0. Find dy dx at ( - 2 , 1). A. 9 B. - 5 3 C. 1 D. 2 E. 5 3 11. Find the maximum and minimum values of the function f ( x )=3 x 2 +6 x - 10 on the interval - 2 x 2.
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ma165-practice-finasecondrevision - MA 165 FINAL EXAM...

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