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GoodmanW98T1 - Math 21H Jan 29 1998 Test#1 Name Read each...

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Math 21H Jan. 29, 1998 Test #1 Name: Read each question carefully, and be sure to show clearly how you got your answers as well as what your answers are. 1. Differentiate the following functions: (a) [9 points] f ( x ) = e x (b) [9 points] f ( x ) = arcsin( e x ) (c) [9 points] f ( x ) = x - x 2. Find these integrals: (a) [9 points] Z e x e x + 1 dx (b) [9 points] Z 1 x 2 + 4 dx 3. [9 points] Solve for x : ln x + ln( x - 1) = ln 2 + ln 6 4. Find the following limits: (a) [9 points] lim x 0 x + sin 3 x x - sin 3 x (b) [9 points] lim x 0 + ln x x (c) [9 points] lim
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