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				   check continuity and differentiability
f(x)= {1/1+ e^1/x} , x is not equal to 0
0   , x=0


6 years ago

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### Answers : (1)

										Ans:Checking the continuity:Left hand limit(LHL) = Right hand limit(RHL) = f(0)$LHL = \lim_{h\rightarrow 0}\frac{1}{1+e^{\frac{-1}{h}}}$$LHL = \lim_{h\rightarrow 0}\frac{e^{\frac{1}{h}}}{1+e^{\frac{1}{h}}}$$LHL = \lim_{h\rightarrow 0}\frac{e^{\frac{1}{h}}+1-1}{1+e^{\frac{1}{h}}}$$LHL = \lim_{h\rightarrow 0}1-\frac{1}{1+e^{\frac{1}{h}}} = 1$$RHL = \lim_{h\rightarrow 0}\frac{1}{1+e^{\frac{1}{h}}} = 0$$f(0) = 0$So, f(x) is not continuous at x = 0.Similarly, you can check the left hand & right hand derivative.$\lim_{h\rightarrow 0}\frac{f(-h)}{-h} = \lim_{h\rightarrow 0}\frac{f(h)}{h}$Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

2 years ago

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