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Question

Find the value of k if
f(x)=⎪ ⎪⎪ ⎪kcosxπ2x,xπ23,x=π2 is continuous at x=π2

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Solution

f(x)=⎪ ⎪⎪ ⎪kcosxπ2x,xπ23,x=π2 is continuous at x=π2
Let π2x=y
x=π2y2
as xπ2,y0
=limy0kcos(π2y2)y=limy0ksiny2y=limy0ksiny2y2×12=k2
f(π2)=limxπ2f(x)3=k2
k=6

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