If f(x)=cos4x−cos5xxsinx,x≠0,f(0)=92 then f(x) at x=0 is

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Continuous

Discontinuous

Not determined

None

answer is A.

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Detailed Solution

Ltx→0f(x)=Ltx→0cos4x−cos5xx21(sinxx) =Ltx→0(1-cos5x)−(1-cos4x)x2 =limx→01-cos 5xx2-1-cos4xx2 =52−422=92 ∴Ltx→0f(x)=f(0)⇒ f is continuous at x=0

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