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1996test2

# 1996test2 - Physical Sciences Division University of...

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Physical Sciences Division University of Toronto at Scarborough MATA26Y January 28, 1997 110 minutes TERM TEST II [20] 1. Find dy/dx in each of the following. Note: Simplification of your answer is not required. (a) y = 3 ( x 2 ) (b) e xy = x 2 + y 2 (c) y = (2 + sin x ) ( x 4 ) (d) y = x 3 1 1 + t 4 dt (e) y = e 3 x - 1 x if x = 0; 3 if x = 0. [15] 2. Compute each of the following limits. Note: Exact answers along with the calculations leading to the answer are ex- pected. NO CREDIT will be given for approximating the limit by evaluatingthe function at nearby points. (a) lim x 0 e x - ln( x + e ) e x - 1 (b) lim x 1 (2 - x ) ( 1 1 - x ) (c) lim x 0 + x 2 ln x [6] 3. What is the 4th degree Taylor polynomial of e 2 x based at 1? Note: Simplification of your answer is not required. [10] 4. Find all local extrema of f ( x ) = x - 3 x 2 / 3 and determine which are local minimums and which are local maximums. [6] 5. The sum of one number and two times a second number is 40. Find the two such numbers with the largest possible product.

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1996test2 - Physical Sciences Division University of...

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