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# PracticeFinal - Math 20A Spring 2008 Practice Final Exam...

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Math 20A Spring 2008 Practice Final Exam Instructor: Oded Yacobi June 6, 2008 Instructions: Turn o/ and put away your cell phones. No notes, calculators, or any other electronic devices are allowed during this exam. Read each question carefully and answer each question completely. Show all your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear ask 20 points. Good luck! 1. Compute dy dx for each of the following functions. a. y = x ln(tan( x )) b. y = x 2 16 x 2 +16 c. y = R x 5 t 2 sinh( t ) dt 2. Consider f ( x ) = 7 x 4 6 x 2 + 1 a. Find f 0 ( x ) and f 00 ( x ) . b. Find all local minima and maxima of f ( x ) . f ( x ) . d. Compute lim x !1 f ( x ) and lim x f ( x ) . e. Draw the graph of f to (b)-(d) and that the concavity of the graph is correct.) 3. Consider the function

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PracticeFinal - Math 20A Spring 2008 Practice Final Exam...

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