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Question

if the function f(x)=(5sinx1)2xlog(1+2x) for x0 is continuous at x=0, find f(0).

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Solution

F is continuous at x=0
f(0)=limx0(5sinx1)2xlog(1+2x)
=limx0(5sinx1)2x2(5sinx1)2xlog(1+2x)x2
=limx0(5sinx1sinx)2sin2xx22log(1+2x)2x
=(limx05sinx1sinx×limx0sinxx)22limx0log(1+2x)2x
=f(0)=(log5)22

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