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MATH 141E Fall 2005 Midterm 1

MATH 141E Fall 2005 Midterm 1 - MATH 141 1 Find(f-1(7 for...

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MATH 141 EXAMINATION I, FORM A OCTOBER 3, 2005 1. Find ( f 1 ) (7) for f ( x ) = p x 3 + x 2 + x + 46 . a) 5 3 b) 7 3 c) 4 3 d) 8 3 e) 1 7 2. Differentiate y = e x + e x e x - e x . 3. Evaluate the integral Z e x cos( e x ) dx . a) - cos( e x ) + C b) sin( e x ) + C c) e x sin( e x ) + C d) - cos( e x ) + x + C e) - e x sin( e x ) + C 4. Use the properties of logarithms to expand ln q a ( b 6 + c 2 ). a) ln( a ) 2 + ln( b 6 + c 2 ) 2 b) ln( a ) 2 + ln(6 b + 2 c ) 2 c) 2 ln( a ) - 2 ln( b 6 + c 2 ) d) 2 ln( a ) + 2 ln( b 6 + c 2 ) e) ln( ab 6 ) + ln( ac 2 ) 5. Solve ln( e x - 7) = 6 for x . 6. Differentiate G ( u ) = ln r 4 u + 3 4 u - 3 . a) G ( u ) = - 7 (4 u + 3)(4 u - 3) b) G ( u ) = - 12 (4 u + 3)(4 u - 3) c) G ( u ) = - 4 u - 3 4 u + 3 d) G ( u ) = r 4 u - 3 4 u + 3 e) G ( u ) = 1 2 ln 4 u + 3 4 u - 3 «
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