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Question

Find whether f is continuous at x=0 or not.If f is continous write 1 otherwise write 0 ?
What is the value of f(x) at x=0

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Solution

f(x)=ln(x)1x
Applying L'Hospital's rule we get
=1x12xx
=2x
Hence as x0 f(x)0.
Thus LHL=RHL=0 which is equal to the value of the f(x) at x=0
Hence f(x) is continuous at x=0

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