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Review2 - MAT135Y 2007-2008 Review Problems for Term-Test 2...

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MAT135Y – 2007-2008 Review Problems for Term-Test 2 The following problems were given at second term-tests 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 Term-Test 2 booklet of that year. For instance [‘03, 6] refers to Problem 6 of Term-Test 2 of December 2003. You can get the answers of the problem by looking at the solutions of the corresponding term-test. These solutions are available online at: http://www.math.utoronto.ca/ponge/teaching/2007-08/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 < 0 , ( x + k ) 2 + (5 k + 2)( x + 1 2 ) if x 0 . 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 y -axis at the point 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) (ln 4) =?.

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Review2 - MAT135Y 2007-2008 Review Problems for Term-Test 2...

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