# 2 - Take-Home Quiz 2 Course Math141 Name NO Work No points...

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Take-Home Quiz 2 Course: Math141 Name: NO Work, No points. Square or Circle your final Answer. 1. Simplify each expression. (a) ln parenleftbigg 1 e 5 parenrightbigg = (b) e ln5 = (c) 3 log 3 20+log 3 50 - log 3 10 = (d) log 2 2 + log 2 24 - log 2 3 = 2. Solve each equation for x . (a) e 2 x - 5 e x - 14 = 0 (b) ln x = 1 - ln (4 x + 1) 1

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3. Find the limit. (a) lim x →∞ 3 e 4 x + e x + e - 4 x 2 e 4 x - e x - e - 4 x = (b) lim x →- 2 - e x/ ( x +2) = (c) lim x →∞ (0 . 3) x = 4. Find the derivatives of the given functions. (a) y = e 2 x 1 + e 2 x (b) f ( x ) = sec ( e x ) - 2 e tan x (c) g ( x ) = sin 2 parenleftBig

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Unformatted text preview: e x )-2 e tan x (c) g ( x ) = sin 2 p e x 2 P 2 (d) f ( x ) = log 5 ( e-x cos (2 x ) ) (e) y = (ln x ) ln x 5. Evaluate the integral. (a) i e √ x √ x dx = (b) i √ ln ( π/ 2) √ ln ( π/ 3) xe x 2 sin p e x 2 P dx = 3 (c) i (2 + e x ) 2 2 e x dx = (d) i e 2 1 3 ln x x dx = (e) i dx x (log 2 x ) 3 = 4...
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