MA 16500 Midterm: Fall 2001, 3
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/100: write your name, student id number, recitation instructor"s name and recitation time in the space provided above. Correct answers with inconsistent work may not be given credit: credit for each problem is given in parentheses in the left hand margin, no books, notes or calculators may be used on this exam. (10) 1. Find the absolute maximum and absolute minimum values of f (x) = x3 3x2 + 3x on the interval [ 1, 2]. abs. max. f ( ) = abs. min. f ( ) = (8) 2. Suppose f is continuous on [2, 5], f is di erentiable on (2, 5) and 1 f (x) 4 for all x in (2, 5). Show that 3 f (5) f (2) 12. (hint: use the mean value theorem. ) Find each of the following limits as a real number, + , or dne (does not exist). (a) lim x 0 sin x x x3 (b) lim x 1+
