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lim x-->0 [cos(sinx)-cosx] / x4

ans: 1/6

3 years ago


Answers : (3)


Using L Hopitals rule

lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d/dx[cos(sin(x))-cos(x)]/x^4 if ([cos(sin(x))-cos(x)]=0 and x=4)

Again since the expression is yielding 0/0 appyling L hopitals rule, 

lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d2/dx2[cos(sin(x))-cos(x)]/x^4 at x=0

Again since the expression is yielding 0/0 appyling L hopitals rule, 

lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d3/dx3[cos(sin(x))-cos(x)]/x^4 at x=0

Again since the expression is yielding 0/0 appyling L hopitals rule, 

lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d4/dx4[cos(sin(x))-cos(x)]/x^4 at x=0

Now Since the expression 4/24= 1/6 .

Hence 1/6 is the answer 


3 years ago







differentiate once more w.r.t. to get the answer

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3 years ago

thanks a lot

3 years ago

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