Limits CMI DOUBT PLEASE SOLVE IT

\lim_{x\rightarrow0}\frac{e^\frac{-1}{x}}{x}

I Cannot Solve it !

I Even Dont Know The Answer !

3 Answers

39
Pritish Chakraborty ·

Limit is undefined....

-EDITED-

Left Hand Limit

Limx→(0-)e-1/xx
= Limh→0e1/h-h

Right Hand Limit

Limx→(0+)e-1/xx
= Limh→0e-1/hh

Clearly LHL ≠RHL, and hence the limit does not exist.

1
Ironman [TDC] ·

Thanks

But It Does not have a particular limit in any side rhl or lhl !!

That's where i was confused.

39
Pritish Chakraborty ·

The LHL is -∞/0 and the RHL is 0/0. Infinitely Irremovable Discontinuity.

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