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Question

Let f(x)=limh0(sin(x+h))ln(x+h)(sinx)lnxh then f(π2) is

A
Equal to 0
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B
Equal to 1
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C
lnπ2
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D
Non - existent
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Solution

The correct option is A Equal to 0
Assuming g(x)=(sinx)lnx
So,
f(x)=g(x)
Taking log of g(x),
lng(x)=lnx×lnsinxg(x)g(x)=lnsinxx+lnx×cotxg(x)=(sinx)lnx[lnsinxx+lnx×cotx]f(π2)=g(π2)=0

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