Calculus I - Fall 2000 - Final Exam - 12/14/00Print 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 ln9() , then 2.19722457733622 is incorrect, but 2ln3() is fine.1. (8) Find the following limits:3x3x3-2x6-lim→1xx981 x-lim→2. (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.