Q.11 The continuous extension of (sin x)*[0,T] a) Graph f(x)= (sin x)*on the interval 0

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Author:Erwin Kreyszig
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solve part d

Q.11 The continuous extension of (sin x)*[0, 7]
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 limf(x) with L'Hôpitaľ's Rule.
x→0+
c) Returning to the graph, estimate the maximum value of f(x) on [0,1].
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.
Transcribed Image Text:Q.11 The continuous extension of (sin x)*[0, 7] 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 limf(x) with L'Hôpitaľ's Rule. x→0+ c) Returning to the graph, estimate the maximum value of f(x) on [0,1]. 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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