Solutions to Exam I (Blue), Ma123,F04

Calculus With Analytic Geometry Seventh Edition

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Math 123 Calculus I Name: 5ol..J..'1)o,-J'J Exam I FaD 2004 RWJ Instructions : Read questions carefully. Please show your work/reasoning so asto help me award you (partial) credit. You will necd to compute a dmvative of a function "using the definition" only in question 5; in all other problems use the various rules/shortcuts that we've discussed Note point values - 105 points are listed. the maximum you may earnis 100. Good luck! "
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1. (20 pts.) Suppose that the distance, in miles, that you've traveled along 1-90 east of Rapid City after 1 minutes is given by 601 f(t)=-, O~t~40. 1+8 a. Compute the average velocity over the time interval from 1 = 12 to 1 = 22 minutes. } ('l "2..) - k ( { ~ - .f:f-=-_~~.:::. 3' ~ - - 1 0- """i~.Jk '2 ~ - 11- b. Compute the instantaneous velocity at time t = 16 minUtes. k I ( t) =- ~ ~ -+ """~8' ) -:~.!_:~:: ..!~~- ( ~..,.. 8' ) 1- C --E:-..I- K ) 1... D 1/. /, ) - ~ """~ Ler.s: - > """'-,,~ f} (1'0/ - -- - - -- --- "'2 f- J.'-\ I~ . -' 1"'i ~. 2 c
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2. (36 pts.) Compute the derivatives of the given functions. Don't waste time simplifying. f( ) 3-2x-x2 a. x= 4x2 -I ,f'()(').= (-2 - '2.l<)(9~1 1) - (:i-2,,-?C'2)(r?C) - - (4?< "L.- ,) '\.. ( X+I ) b. g(x) = - (2x-5) x+2 I t - ( ~ C ~ J) (Lx-5) -l- ( ~ ) '2...
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