MAT 17A Final: Final17A Exam Fall 2013
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1. (30 points) evaluate each limit. (a) lim x x2e x (b) lim x 0. X2 + 8 3 x + 1 (c) lim x 1 (d) lim x cos2 x x. 5x 1 (f) lim x 0 (ex + x)1/x. 3: (20 points) find dy dx (a) y = (ln x)2x. You need not simplify your answer. (b) y = (ln(1 x3))2. 4 (c) y = (3x2 1)(5x4 10x) (d) y = log3. 5: (15 points) a rectangle has its base on the x-axis, its lower left corner at (0, 0), and its upper right corner on the curve y = 1 x (a) express the perimeter of the rectangle as a function of x, namely p(x). (b) what is the domain of p(x)? (c) find the smallest perimeter of the rectangle. 6: (20 points) consider the function f (x) = (x + 1)2. 1 + x2 (a) determine where the function is increasing and where it is decreasing.
