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If f(x)={e^(1/x) ,1 ifx!=0ifx=0 F...

If `f(x)={e^(1/x) ,1` `ifx!=0ifx=0` Find whether `f` is continuous at `x=0.`

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`f(x)= {e^(1/x)` when `x!=0` and ` 1` when `x=0`
For the continuity at `x=0`
`f(0)=1`
`text { LHL }=lim _{x -> 0} f(x) `
`text{LHL}=lim _{h -> 0} f({0}-h) `
`text{LHL}=lim _{h -> 0} e^(1/(0-h))`
`text{LHL} = lim _{h -> 0} e^(-1/h)=0`
Now,
...
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