M106 Practice Exam 3

[Note: These problems appeared on my M106 exams in the fall of 1995.]

Instructions: Show all of your work and clearly explain your answers. This is particularly important on problems with a numerical answer, to allow the possibility of partial credit. No books are allowed during the exam, but you may use your calculator.

Problem [1] Suppose that f(x) is a differentiable function such that f(2)=3, f'(2)=5 and f'(3)=7.
Problem [2] Suppose the graph below gives the derivative g(x) of some function y = G(x). Graph goes here.

Problem [3] Consider the limit as h approaches 0 of [ln(e+h)-1]/h.
Problem [4] Let h(x) = x2x.
Problem [5] Farmer Brown wants to fence off three sides of a rectangular area; the fourth side runs along a river and does not need a fence. She wants there to be 5000 square yards of land in the rectangle. What are the dimensions of the rectangle needing the least amount of fencing?