The point P(1, 0) lies on the curve y = sin(14pi)/ x (a) If Q is the point

x, sin14𝜋/x

, find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 0

Correct: Your answer is correct. (ii) 1.5 -1.7321

Correct: Your answer is correct. (iii) 1.4 0

Correct: Your answer is correct. (iv) 1.3 2.2104

Correct: Your answer is correct. (v) 1.2 -4.3301

Correct: Your answer is correct. (vi) 1.1 7.5575

Correct: Your answer is correct. (vii) 0.5 0

Correct: Your answer is correct. (viii) 0.6 2.1651

Correct: Your answer is correct. (ix) 0.7 0

Correct: Your answer is correct. (x) 0.8 5

Correct: Your answer is correct. (xi) 0.9 9.8481

Correct: Your answer is correct. Do the slopes appear to be approaching a limit? As x approaches 1, the slopes do not appear to be approaching any particular value

Correct: Your answer is correct. . (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 frequent oscillations

Correct: Your answer is correct. of the graph. The tangent is so steep at P that we need to take x-values closer

Correct: Your answer is correct. to 1 in order to get accurate estimates of its slope. (c) By choosing appropriate secant lines, estimate the slope of the tangent line at P. (Round your answer to two decimal places.)