101-1999&2000-2-F10-May2000 - I:rZwait Univer~ity D.ep...

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:rZwait Univer~ity , D.ep ~~ of I\1ath.&Comp.Sd. I\1ath. 101 Final Exuln. Date: I\1ay 24, 2000 Duration: Two hours Calculators, I\1obiIePhones and Pagers are not allowed Answer the following questions '-i~ (3 pts.) Let x ,if x:S;-1f, f (x) = x x + sinx , if -1f < x < 0, 1 - 2 - x , if x > o. Classify the discontinuities of f as removable, jump or infinite. : (3 pts.) Find the horizontal asymptotes, if any, for the graph of f (x) = V'x + 2 - 2 x+2 . 3. (3 pts.) Use the definition of the derivative to find J' (1), where f (x) = V'3x + 1. . x 4. (3 pts.) Use differentials to approxjmate the change in y = _3/3---;-;:)1 when x changes from 5 to 4.9. 5. Let f(x) = x3 + 3x2 - 9x + 1. (a) (3 pts.) Find the local extrema of f. (b) (3 pts.) Find the intervals on wh.ich the graph of {'is concave upward. What 'are the points of inflection? O. J 4: pts.) Find the dimensions of the rectangle of maximum area whose diagonal is 2 ft. 1 (c) J .Jl- x2 dx. -1 7. Evaluate the following integrals (3 points each): 3 (b) J Ix - 21 dx. 1 (a) j(1+cos2x)3_Sin2Xdx~ ., ,d_ ~.
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