2001FallFinal - Calculus I Fall 2001 Final Exam 13 problems on 11 pages plus two scratch pages 100 points 2 hours 30 minutes Write your answers directly

# 2001FallFinal - Calculus I Fall 2001 Final Exam 13 problems...

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Calculus I - Fall 2001 - Final Exam - 12/12/0113 problems on 11 pages plus two scratch pages.100 points, 2 hours 30 minutes. Write your answers directly on this sheet. Continue on back if necessary.Support your answers and show all your work. Closed notes, closed book, no calculators.Exact answers are required: For example, if the answer is π, then 3.14 is incorrect.1. (5) Use the limit definition of the derivative to show that the derivative of f t( )1t3+=is f 't( )1t3+()2=. 2. (8) Find the following limits:2xex 1+lim0x1x+()csc x( )lim0xx2cos x( )1-limx4x72x2-5+11x7x3+8x-lim3. (15) Find xsin x( )x2ddxx8x4-7x2+1x-ddθcosθ(29(292ddxyddwhere yx2xf "(t)where f t( )A cosϖt(29-==
4. (5) Find the equation of the tangent line to the graph of yx2=at the point (2,4). 5. (5) Use linear approximation to approximate 38.01. Use the fact that 3826. (10) A ladder of length 15 feet is leaning against a house. The foot of the ladder is 9 =.