Q.

If the function f(x)=cos (sin x)-cos xx4 is continuous at each point in its domain & f(0)=1k, then k = 

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answer is 6.

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Detailed Solution

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f(0)=Ltx0 cos (sin x)-cos xx4

 f(0)=Ltx0-2sinsinx+x2sinsinx-x2x4  =Ltx0 -2sin x+x2sin sin x-x2x4=Ltx0x2-sin2 xx4=Ltx0-2x2[sin x-x]x3 as x0sin xx  =Ltx0-cos x+13x2=+16k=+6

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