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(c) By choosing appropriate secant lines, estimate the slope of the tangent line at P. (Round your answer to two decimal places.)

(c) By choosing appropriate secant lines, estimate the slope of the tangent line at P. (Round your answer to two decimal places.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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14л The point P(1, 0) lies on the curve y = sin (a) If Q is the point sin 14x find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 -1.7321 (iii) 1.4 (iv) 1.3 2.2104 (v) 1.2 -4.3301 (vi) 1.1 7.5575 (vii) 0.5 (viii) 0.6
Transcribed Image Text:14л The point P(1, 0) lies on the curve y = sin (a) If Q is the point sin 14x find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 -1.7321 (iii) 1.4 (iv) 1.3 2.2104 (v) 1.2 -4.3301 (vi) 1.1 7.5575 (vii) 0.5 (viii) 0.6
(viii) 0.6 2.1651 (ix) 0.7 (x) 0.8 (xi) 0.9 9.8481 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes do not appear to be approaching any particular value (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 of the graph. The tangent is so steep at P that we need to take x-values closer V 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.)
Transcribed Image Text:(viii) 0.6 2.1651 (ix) 0.7 (x) 0.8 (xi) 0.9 9.8481 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes do not appear to be approaching any particular value (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 of the graph. The tangent is so steep at P that we need to take x-values closer V 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.)
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