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(3) Qis the point (x, (1) 2 () 1.5 () 1.4 (N) 1.3 € 2 (v) 1.2 (vi) 1.1 (vi) 0.5 (vi) 0.6 (xx) 0.7 (x) 0.8 (x) 0.9 find the slope of the secant line PQ (correct to four decimal places) for the following values of x. Do the slopes appear to be approaching a limit? As x approaches 1, the slopes -Select-

(3) Qis the point (x, (1) 2 () 1.5 () 1.4 (N) 1.3 € 2 (v) 1.2 (vi) 1.1 (vi) 0.5 (vi) 0.6 (xx) 0.7 (x) 0.8 (x) 0.9 find the slope of the secant line PQ (correct to four decimal places) for the following values of x. Do the slopes appear to be approaching a limit? As x approaches 1, the slopes -Select-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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.
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