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Examine the continuity of the following functions at indicated points.f(x)={((e^(1/x)-1)/(e^(1/x)+1)if xne0 at x=0),(0 if x=0):} |
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Answer» Solution :f(0)=0 `L.H.L. =lim_(hto0)(e^(-1/h)-1)/(e^(-1/h)+1)=-1` `R.H.L.=lim_(hto0)(e^(1/h)-1)/(e^(1/h)+1)` `=lim_(hto0)(1-e^(1/h))/(1+e^(1/h))=1` Thus `L.H.L NE R.H.L. ne f(0)` HENCE f(X) is discontinuous at the origin. |
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