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Q.

If  f:R→R  defined by f(x)=a2cos2x+b2sin2x      (x≤0).eax+b                                                 (x>0)   is a continuous function , then

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a

b=2log|a|

b

2b=log|a|

c

b=log|2a|

d

b2=log|2a|

answer is A.

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Detailed Solution

LHL=limx→0-a2cos2x+b2sin2x=a2 RHL=limx→0+eax+b=eb LHL=RHL eb=a2⇒b=2loga
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