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. x *0 x = 0. Let f(x) = {1*/*. (a) Use a graphing utility to graph f in the viewing window -3 ≤x≤ 3,-2 ≤ y ≤ 2. What is the domain of f? (b) Use the zoom and trace features of a graphing utility to estimate lim f(x). (c) Write a short paragraph explaining why the function f is continuous for all real numbers.

. x *0 x = 0. Let f(x) = {1*/*. (a) Use a graphing utility to graph f in the viewing window -3 ≤x≤ 3,-2 ≤ y ≤ 2. What is the domain of f? (b) Use the zoom and trace features of a graphing utility to estimate lim f(x). (c) Write a short paragraph explaining why the function f is continuous for all real numbers.

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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SECTION PROJECT Using Graphing Utilities to Estimate Slope Let f(x) = {1*²* [xx, x = 0 x = 0. (a) Use a graphing utility to graph f in the viewing window -3 ≤ x ≤ 3, -2 ≤ y ≤ 2. What is the domain of f? (b) Use the zoom and trace features of a graphing utility to estimate lim f(x). x-0 (c) Write a short paragraph explaining why the function f is continuous for all real numbers. (d) Visually estimate the slope of f at the point (0, 1). (e) Explain why the derivative of a function can be approximated by the formula f(x + Ax)-f(x - A.x) 24.x for small values of Ax. Use this formula to approximate the slope of f at the point (0, 1). f'(0) S f(0+ Ax)-f(0 - A.x) 2Δ.x f(Ax)-f(-Ax) 2Δ.x What do you think the slope of the graph of f is at (0, 1)? (f) Find a formula for the derivative of f and determine f'(0). Write a short paragraph explaining how a graphing utility might lead you to approximate the slope of a graph incorrectly. (g) Use your formula for the derivative of f to find the relative extrema of f. Verify your answer using a graphing utility. FOR FURTHER INFORMATION For more information on using graphing utilities to estimate slope, see the article "Computer-Aided Delusions" by Richard L. Hall in The College Mathematics lournal To view this article go to Math Articles.com
Transcribed Image Text:SECTION PROJECT Using Graphing Utilities to Estimate Slope Let f(x) = {1*²* [xx, x = 0 x = 0. (a) Use a graphing utility to graph f in the viewing window -3 ≤ x ≤ 3, -2 ≤ y ≤ 2. What is the domain of f? (b) Use the zoom and trace features of a graphing utility to estimate lim f(x). x-0 (c) Write a short paragraph explaining why the function f is continuous for all real numbers. (d) Visually estimate the slope of f at the point (0, 1). (e) Explain why the derivative of a function can be approximated by the formula f(x + Ax)-f(x - A.x) 24.x for small values of Ax. Use this formula to approximate the slope of f at the point (0, 1). f'(0) S f(0+ Ax)-f(0 - A.x) 2Δ.x f(Ax)-f(-Ax) 2Δ.x What do you think the slope of the graph of f is at (0, 1)? (f) Find a formula for the derivative of f and determine f'(0). Write a short paragraph explaining how a graphing utility might lead you to approximate the slope of a graph incorrectly. (g) Use your formula for the derivative of f to find the relative extrema of f. Verify your answer using a graphing utility. FOR FURTHER INFORMATION For more information on using graphing utilities to estimate slope, see the article "Computer-Aided Delusions" by Richard L. Hall in The College Mathematics lournal To view this article go to Math Articles.com
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