. 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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