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Question

If f(x)={a2cos2x+b2sin2x,x0eax+b,x>0 f(x) is continuous at x=0 then

A
2log|a|=b
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B
2log|b|=e
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C
loga=2log|b|
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D
a=b
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Solution

The correct option is A 2log|a|=b
Given the function f(x) is continuous at x=0, then
limx0f(x)=limx0+f(x)
or, limx0(a2cos2x+b2sin2x)=limx0+(eax+b)
or, a2=eb
or, b=2log|a|.

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