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Question

If f(x)=1cosxx,x0k,x=0 is continuous at x=0, then the value of k is

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Solution

For continuity of f(x) at x=0, we must have,
f(0)=limx0f(x)
=limx01cosxx [00 form]
Applying L hospital's rule
=limx0sinx1=sin0=0
k=0

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