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MTH 140 Final: MTH140 - W2018 Final (Solution)

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turquoisegnu128
31 Jan 2019
School
Ryerson University
Department
Mathematics
Course
MTH 140
Professor
All

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Document Summary

Then g (x) is equal to: (multiple choice question) let g(x) = 1: 3x2 sec(ex3, sec(ex3, sec(ex) 2. (multiple choice question) the value of lim x 1 x1/(1 x) is: 1. 1 e: does not exist, e, none of these. 3. (multiple choice question) let f (x) = sinh(ln x). Then f (x) is equal to: cosh(ln x: cosh( 1 x) 1 x2 x: 1 , cosh(ln x) Write the (capital) letter of the answer in this box. Only the answer in the box will be marked. 1 sin(ln x) x dx dx = 2 x. Solution: let u = ln x = 1. 2 ln 1 = 0 and when x = e , y = 1 e . 0 = 2(0 1) = 2 sin(u) du sin(ln x) Solution: let u = x3 + 1, so du = 3x2 dx and x3 = u 1.

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3. (18 pts) MULTIPLE CHOICE ! ! ! A table of values for f(x) and f'(x) is shown below. Suppose that f is a one-to-one function and f (x) is its inverse. f' x 1 3 4 f (x) 3 4 6 (x) 4 5 3 CIRCLE THE CORRECT ANSWER IN EACH PART. (I) Evaluate f-1 (f (x)) at x = 3. (a) 1 ; (b) 3; (c) 6; (a) 4; (e) DOES NOT EXIST; (£) NONE OF THE PREVIOUS ANSWERS. (11) Evaluate e f (f (x)) at x = 3. (a) 6 ; (b) 25; (c) 5; (d) 15; (e) DOES NOT EXIST ; () NONE OF THE PREVIOUS ANSWERS. (111) Evaluate e In (f (x)) at x = 3. (e) DOES NOT EXIST; (f) NONE OF THE PREVIOUS ANSWERS. (IV) Evaluate f-1 (x) at x = 3. (a) 4; (a) 4 ; (b) 1; (b) 1 ; (com () 5; (d) 5; (e) DOES NOT EXIST; () NONE OF THE PREVIOUS ANSWERS. (v) Evaluate -? (x) at x = 3. (a) 1 ; (b) 4; (e) 5; () NONE OF THE PREVIOUS ANSWERS. (VI) Find the average rate of chnage of f over the interval (1, 3). (a) 2 ; (b)1; (c) ; (a) 5; (e) DOES NOT EXIST; () NONE OF THE PREVIOUS ANSWERS.