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Question

Let f be the function defined as f(x)=cos2xsin2x1x+11, if x0k, if x=0, if x0, is continuous at x=0
Find the value of k

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Solution

RHL=limhof(x+h)

RHL=limhof(o+h)
=limho(cos2hsin2h1h+11)
=limho(1sin2hsin2h1h+11)(h+1+1h+1+1)
=limho(2sin2h(h+1+1)h+11)
=limho2((sinhh)sinh(h+1+1))

=2102=0
forcontinuityLHL=RHL=f(0)
k=0


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