2000FallFinal - Calculus I Fall 2000 Final Exam Print your name 10 problems 100 points 2 hours 30 minutes Write your answers directly on this sheet

2000FallFinal - Calculus I Fall 2000 Final Exam Print your...

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Calculus I - Fall 2000 - Final Exam - 12/14/00 Print your name: 10 problems, 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. Exact answers are required: For example, if the answer is 2 , then 1.4142 is incorrect. If the answer is ln 9 ( ) , then 2.19722457733622 is incorrect, but 2ln 3 ( ) is fine. 1. (8) Find the following limits:3x3x3-2x6-lim1xx981 x-lim2. (9) a) State the definition of the derivative f 'x( )b) Let f x( )32x=. Use the definition to show that f 'x( )2x2=. 3. (15) Find . 3 - :
4. (9) Find the slope of the tangent line of the curve given by the parametric equationyt2t+1+=, xt2t-=at the point where x34=, y34=. You will have to find 5. (5) Suppose the differentiable function f is defined on the interval [0,2], with f(1)=2, f '(1) = 10. Use linear approximation to find an approximate value for f(1.1).6. (10) Two cars, an Audi A and a Buick B, are approaching an intersection of two t .

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