Chapter 3.5, Problem 47E

Find The Derivatives.

derivatives

14 The point P(1, 0) lies on the curve y sin (a) of Q is the point (x, sin(14)). find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (1) 2 () 1.5 () 1.4 (v) 1.3 3 3 (v) 1.2 (vi) 1.1 (vi) 0.5 (vi) 0.6 (xx) 0.7 (x) 0.8 (x) 0.9 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes-Select- (b) Use a graph of the curve to explain why the slopes of the secant lines in part (a) are not close to the slope of the tangent line at P. We see that problems with estimation are caused by the --Select- of the graph. The tangent is so steep at P that we need to take x-values (c) By choosing appropriate secant lines, estimate the slope of the tangent line at P. (Round your answer to two decimal places.) Solert. to 1 in order to get accurate estimates of its slope.