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Question

If the function f defined on (π6,π3) by f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪2cosx1cotx1,xπ4k,x=π4 is continuous, then k is equal to?

A
12
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B
1
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C
12
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D
2
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Solution

The correct option is A 12
function should be continuous at x=π4

limxx4f(x)=f(π4)

limxx42cosx1cotx1=k

limxπ42sinxcosec2x=k (Using L'^o pital rule)

limxπ42sin3x=k

k=2(12)3=12.

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