finB05

# finB05 - a limit. C) State the derivative of sin-1 ( x )...

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MAC 2311 Dec 14, 2005 Final Exam B [review of early topics] Prof. S. Hudson Name Show all your work and reasoning for maximum credit. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper (but hand it back in). 1) (20 pts) Compute y 0 : a) y = sec x tan x b) y = tan 4 ( x 3 ) c) 5 y 2 + sin( y ) = x 2 d) y = 2 x 1

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2) (15 pts) Compute: a) lim x + e x +2 x 2 3 e x +4 x 4 b) y 00 given that y = ln | 2 x | . c)lim x + ( 2+ x x ) 2 x 3)(15 pts) Find the local linear approximation to e x at x 0 = 0. Use it to approximate e . 05 . 2
4) (10 pts) Find parametric equations for the portion of the circle that lies in the third quadrant, oriented counterclockwise. 5) (15 pts) CHOOSE ONE; A) State and prove the Product Rule B) Prove that the derivative of sin( x ) is cos( x ) using the deﬁnition of derivative, and

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Unformatted text preview: a limit. C) State the derivative of sin-1 ( x ) and prove your answer as done in class (and simplify using a triangle). 3 6) (15 pts) Answer TRUE or FALSE: If f is a polynomial, then g ( x ) = f ( e x ) is dierentiable. If lim x a f ( x ) = lim x a g ( x ) = L , then lim x a [ f ( x ) + 1] g ( x ) = L 2 + L tan-1 ( x ) has two dierent horizontal asymptotes. f ( x ) = 2-x has an inverse function. f ( x ) = ( x 2 + x + 1)-1 is continuous. 7) (10 pts) If a particle moves at constant velocity, what can you say about its position vs time curve? BONUS (5 pts): Compute the tricky integral, R sec( x ) dx , showing all the steps. 4...
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## This note was uploaded on 05/28/2011 for the course MAC 2311 taught by Professor Staff during the Spring '08 term at FIU.

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finB05 - a limit. C) State the derivative of sin-1 ( x )...

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