MATH 180 Study Guide - Final Guide: Quotient Rule
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Solution: first we note that cx + 5 and x2 + x 3c are polynomials and are continuous on the intervals x > 1 and x < 1, respectively. We must determine the constant c so that f (x) is continuous at x = 1. Recall that for continuity at x = 1 we need lim f (x) to exist. x 1. In order for lim x 1 f (x) to exist we need the one-sided limits to be the same. That is, we need: lim x 1+ f (x) = lim x 1 f (x) c + 5 = 2 3c. Problem 2 solution: find an equation for the tangent line to the graph of the function f (x) = sin(x) at the point x = /4. Solution: the derivative of f (x) at x = of f is f (x) = cos(x). 4 is the slope of the tangent line.
