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Math242E106

# Math242E106 - (a g(b g 2(10 points Simplify sinh ln 2-ln 4...

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FORM A MATH 242, Fall 2006 Exam 1: October 4, 10:10-11:00 Only the blue book will be graded. On the front cover, please write Form A clearly, along with your name and section number. Please start each problem on a new page, circle final answers, and cross out incorrect work. Unless otherwise noted, you must justify all answers to receive full credit. You may not use calculators, notes, or any other kinds of aids. 1. (5 points each) Shown here is a graph of y = f ( x ) . Let g ( x ) = f - 1 ( x ) . Find each value, if it exists. Remember to explain your answers.
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Unformatted text preview: (a) g ( ) (b) g ( ) 2. (10 points) Simplify sinh ( ln 2-ln 4 ) to a rational number. 3. (10 points each) Find y in each case. (a) y = ln ( x 2 2 x ) (b) y = 1 e cos x 4. (15 points each) Evaluate each limit. (a) lim x → x tan-1 ± 1 x ¶ (b) lim x → tanh ( 5 x 2 ) x 2 5. (15 points each) Evaluate each integral. (a) Z 4 x + 1 4 x 2 + 1 dx (b) Z e-x √ 1 + e-x dx d dx ‡ sin-1 x · = 1 √ 1-x 2 d dx ‡ tan-1 x · = 1 1 + x 2...
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