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Question

For what value of k is the function
fx=sin 5x3x, ifx0 k , ifx=0is continuous at x=0?

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Solution

Given:
fx=sin5x3x, if x0k, if x=0
If fx is continuous at x = 0, then
limx0fx = f0
limx0sin5x3x= k
limx05 sin5x3×5x= k
53limx0sin5x5x= k
53×1= k
k=53

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