The continuous extension of (sin x)^x [0,π] a) Graph f(x)= (sin x)^x on the interval 0 ≤ x ≤ π. What value would you assign to f(x) to make it continuous at x = 0? b) Verify your conclusion in part (a) by finding limx→0+ f(x) with L’Hôpital’s Rule.
The continuous extension of (sin x)^x [0,π] a) Graph f(x)= (sin x)^x on the interval 0 ≤ x ≤ π. What value would you assign to f(x) to make it continuous at x = 0? b) Verify your conclusion in part (a) by finding limx→0+ f(x) with L’Hôpital’s Rule.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The continuous extension of (sin x)^x [0,π]
a) Graph f(x)= (sin x)^x on the interval 0 ≤ x ≤ π. What value would you assign to f(x) to make it continuous at x = 0?
b) Verify your conclusion in part (a) by finding limx→0+ f(x) with L’Hôpital’s Rule.
c) Returning to the graph, estimate the maximum value of f(x) on [0, π].
About where is max f(x) taken on?
d) Sharpen your estimate in part (c) by graphing ƒ in the same window to see where its graph crosses the x-axis. To simplify your work, you might want to delete the exponential factor from the expression for f' and graph just the factor that has a zero.
![Q.11 The continuous extension of (sin x)*[0,x]
a) Graph f(x)= (sin x)*on the interval 0 <x < n. What value would you
assign to f (x) to make it continuous at x = 0?
b) Verify your conclusion in part (a) by finding lim f (x) with L'Hôpital's Rule.
x-0
c) Returning to the graph, estimate the maximum value of f(x) on [0, 7].
About where is max f (x) taken on?
d) Sharpen your estimate in part (c) by graphing f in the same window to see
where its graph crosses the x-axis. To simplify your work, you might want to
delete the exponential factor from the expression for f'and graph just the
factor that has a zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98af15d4-5945-46a7-8313-585cd7b54406%2Fa4c8d102-e035-4fb3-91e7-134d16fadceb%2Fr0rcds_processed.png&w=3840&q=75)
Transcribed Image Text:Q.11 The continuous extension of (sin x)*[0,x]
a) Graph f(x)= (sin x)*on the interval 0 <x < n. What value would you
assign to f (x) to make it continuous at x = 0?
b) Verify your conclusion in part (a) by finding lim f (x) with L'Hôpital's Rule.
x-0
c) Returning to the graph, estimate the maximum value of f(x) on [0, 7].
About where is max f (x) taken on?
d) Sharpen your estimate in part (c) by graphing f in the same window to see
where its graph crosses the x-axis. To simplify your work, you might want to
delete the exponential factor from the expression for f'and graph just the
factor that has a zero.
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