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Unformatted text preview: MAT135Y 20072008 Review Problems for TermTest 2 The following problems were given at second termtests of previous academic years. For each problem there is a year followed by a number. The year is the year at which the problem was given and the number is the number of the problem in the TermTest 2 booklet of that year. For instance [03, 6] refers to Problem 6 of TermTest 2 of December 2003. You can get the answers of the problem by looking at the solutions of the corresponding termtest. These solutions are available online at: http://www.math.utoronto.ca/ponge/teaching/200708/MAT135/MAT135.html . The sign ? indicates that the problem is chalenging. Problem on Chapter 2 Problem 1 (03, 6) . Let f ( x ) = sin kx sin 2 x if x < , ( x + k ) 2 + (5 k + 2)( x + 1 2 ) if x . Find the value of the constant k so that f is continuous everywhere. (a) 0 (b) 2 (c) 1 (d) 5 2 (e) 1 2 . Problems on Chapter 3 Problem 2 (03, 7) . The line tangent to the curve x 2 + 3 y 2 = 1 at the point ( 1 2 , 1 2 ) intercept the yaxis at the point (a) (0 , 1 3 ) (b) (0 , 1 2 ) (c) (0 , 4 3 ) (d) (0 , 1) (e) (0 , 2 3 ) . Problem ? 3 (02, 18) . Let f ( n ) ( a ) denote the n th derivative of f at a . If f ( x ) = e 2 x cosh(2 x )sinh(4 x ), then f (20) (ln4) =?. (a) 2 74 + 2 46 2 30 (b) 2 72 + 2 46 2 32 (c) 2 72 + 2 44 2 32 (d) 2 72 + 2 46 2 30 (e) 2 74 + 2 44 2 30 . Problem 4 (04, 7) . Let f ( n ) ( a ) denote the n th derivative of f at a . If f ( x ) = sin2 x , then f (6) ( 12 ) =. (a) 16 (b) 32 (c) 64 (d) 0 (e) 16 ....
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This note was uploaded on 09/14/2008 for the course MAT 135 taught by Professor Lam during the Spring '08 term at University of Toronto Toronto.
 Spring '08
 LAM

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