W14mThe point P(1, 0) lies on the curve y = sin14m(a) If Q is the pointfind 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) 1.32.2104(v) 1.2-4.3301(vi) 1.17.5575(vii) 0.5(viii) 0.62.1651(ix) 0.7a3:38 PM60°F (iv) 1.32.2104(v) 1.2-4.3301(vi) 1.17.5575(vii) 0.5(viii) 0.62.1651(ix) 0.7(х) 0.8(хi) 0.99.8481Do the slopes appear to be approaching a limit?As x approaches 1, the slopes do not appear to be approaching any particular value v(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 oscillationsneed to take x-values closerof the graph. The tangent is so steep at P that wev 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.)9.85

Answered: The point P(1, 0) lies on the curve y =…

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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Question

W14m
The point P(1, 0) lies on the curve y = sin
14m
(a) If Q is the point
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
2.1651
(ix) 0.7
a
3:38 PM
60°F

(iv) 1.3
2.2104
(v) 1.2
-4.3301
(vi) 1.1
7.5575
(vii) 0.5
(viii) 0.6
2.1651
(ix) 0.7
(х) 0.8
(хi) 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 v
(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
need to take x-values closer
of the graph. The tangent is so steep at P that we
v 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.)
9.85

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Introduction:

Because a secant line is also a line, we use the slope of a line formula to find the slope of a secant line formula. Depending on the information available, there are several formulas for calculating the slope of a secant line. Consider the curve $y = f (x)$ and the second line drawn to this curve.