practice-quiz2-sol

practice-quiz2-sol - AMS 151 (Fall, 2009) Joe Mitchell...

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AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Practice Problems for Quiz # 2 – Solution Notes 1. Solve for x : 4 · 2 2 x - 1 - 3 · 5 x = 0. 4 · 2 2 x - 1 = 3 · 5 x ln 4 + ln 2 2 x - 1 = ln 3 + ln 5 x ln 4 + (2 x - 1) ln 2 = ln 3 + x ln 5 (2 ln 2 - ln 5) x = ln 3 - ln 4 - ln 2 x = ln 3 - ln 4 - ln 2 2 ln 2 - ln 5 = ln(3 / 8) ln(4 / 5) 2. Determine which function has a larger value as x → ∞ : (a). f ( x ) = 5 · x 2 - 57 x or g ( x ) = 0 . 002 · (1 . 001) x g ( x ) grows faster, since is is exponential (proportional to 1 . 001 x ), while f ( x ) is polynomial (grows like x 2 ). (b). f ( x ) = log 4 x or g ( x ) = 3 · log 2 x 3 f ( x ) grows faster, since it grows like log 4 x , while g ( x ) grows like log 2 x (a lower power of logarithm). 3. Find the inverse function of y = g ( t ) = 3 e t +4 - 2. 2 + y 3 = e t +4 ln( 2 + y 3 ) = t + 4 t = ln( 2 + y 3 ) - 4 Thus, g - 1 ( y ) = ln( 2+ y 3 ) - 4. 4. Let
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This note was uploaded on 02/07/2010 for the course AMS 151 taught by Professor Zhang during the Fall '08 term at SUNY Stony Brook.

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practice-quiz2-sol - AMS 151 (Fall, 2009) Joe Mitchell...

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