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Show that \(\lim\limits_{\text x \to0}\cfrac1{\text x} \) does not exist.

lim(x→0) 1/x
 

1 Answer

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Best answer

Let x = 0 + h for x tending to 0+

Since x→ 0, h also tends to 0

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

Let x=0 - h for x tending to 0-

Since x→0, h also tends to 0.

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

Thus, \(\lim\limits_{\text x \to0}\cfrac1{\text x} \) does not exist.

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