Show that lim(x→0) e^ -1/x does not exist.

Question

Show that \(\lim\limits_{\text x \to0}e^{-1/\text x} \) does not exist.

lim(x→0) e ^-1/x

Answer 1

 \(\lim\limits_{\text x \to0}e^{-1/\text x} \) 

lim(x→0) e ^-1/x

Left Hand Limit(L.H.L.):

Right Hand Limit (R.H.L.):

[Formula \(\cfrac1\infty=0,\) anything to the power infinity is also infinity. Thus \(\cfrac{1}{e^{\infty}}=\cfrac1{\infty}=0\)]

= 0

Since