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33. T Slope of tangent line Given the function f(x) = 1 - cos x and the points A(π/2, f(π/2)), B(π/2 +0.05, f(π/2 +0.05)), C(π/2+0.5, f(π/2+0.5)) and D(π, f(n)) (see figure), find the slopes of the secant lines through A and D, A and C, and A and B. Use your calculations to make a conjecture about the slope of the line tangent to the graph of fat x = π/2. y 2 L +0.5 0 +0.05 y = 1- cos x X

33. T Slope of tangent line Given the function f(x) = 1 - cos x and the points A(π/2, f(π/2)), B(π/2 +0.05, f(π/2 +0.05)), C(π/2+0.5, f(π/2+0.5)) and D(π, f(n)) (see figure), find the slopes of the secant lines through A and D, A and C, and A and B. Use your calculations to make a conjecture about the slope of the line tangent to the graph of fat x = π/2. y 2 L +0.5 0 +0.05 y = 1- cos x X

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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33. T Slope of tangent line Given the function f(x) = 1 − cos x and the points A(π/2, ƒ(π/2)), B(π/2 +0.05, ƒ(π/2 +0.05)), C(π/2 +0.5, ƒ(π/2 + 0.5)) and D(π, ƒ(π)) (see figure), find the slopes of the secant lines through A and D, A and C, and A and B. Use your calculations to make a conjecture about the slope of the line tangent to the graph of fat x = π/2. f +0.5 +0.05 2- FEIN ㅠ y = 1- cos x X
Transcribed Image Text:33. T Slope of tangent line Given the function f(x) = 1 − cos x and the points A(π/2, ƒ(π/2)), B(π/2 +0.05, ƒ(π/2 +0.05)), C(π/2 +0.5, ƒ(π/2 + 0.5)) and D(π, ƒ(π)) (see figure), find the slopes of the secant lines through A and D, A and C, and A and B. Use your calculations to make a conjecture about the slope of the line tangent to the graph of fat x = π/2. f +0.5 +0.05 2- FEIN ㅠ y = 1- cos x X
Expert Solution
Step 1

The slope between two points of a line (x1,y1) and (x2,y2) is given by the equation;

slope(m)=y2-y1x2-x1

 

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