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Q. Determine f(0) so that the function f(x) defined by f (x) = 4x-13sinx4 log1+x23

becomes continuous at x = 0. Explain the steps in details.

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Solution

Dear student
for f(x) to be continuous at x=0, we must havelimx0f(x)=f(0)f(0)=limx0f(x)=limx04x-13sinx4log1+x23f(0)=limx04x-1x3sinx44×x4log1+x23x23×113=f(0)=loge4314×13=12loge43
Regards

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