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(a) If Q is the point (x, sin 16)), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249

(a) If Q is the point (x, sin 16)), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249

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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CIRCLE EACH ANSWER WRITE OR TYPE NEATLY answer in four decimal places

CIRCLE EACH ANSWER WRITE OR TYPE NEATLY answer in four decimal places

(a) If Q is the point (x, sin10), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. () 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249 (iv) 1.3 1.1757 (v) 1.2 |-1.0825 (vi) 1.1 1.0998 (vii) 0.5 (viii) 0.6 0.6186 (ix) 0.7 1x (x) 0.8 0.3337 (xi) 0.9 |-0.5843 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes approach 1 (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 discontinuities vx of the graph. The tangent is so steep at P that we need to take x-values -Select-- 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:(a) If Q is the point (x, sin10), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. () 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249 (iv) 1.3 1.1757 (v) 1.2 |-1.0825 (vi) 1.1 1.0998 (vii) 0.5 (viii) 0.6 0.6186 (ix) 0.7 1x (x) 0.8 0.3337 (xi) 0.9 |-0.5843 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes approach 1 (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 discontinuities vx of the graph. The tangent is so steep at P that we need to take x-values -Select-- 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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