How to solve that Limit without graphing ? $limx->0^+$ $1/x$ = $oo$ $limx->0^-$ $1/x$ $-oo$

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Answer 1 · 2018-04-20T15:28:00

Plug in a number for $x$ such as $0.0000001$ which is $0^+$

Given: $lim x-> 0^+ 1/x = oo; " "lim x-> 0^- 1/x = -oo$

Without graphing you can plug in a value that approaches $0^+$ and $0^-$ .

$x->0^+$ means approach from the right side (positive) of zero:
Let $x = .01; " " 1/x = 100$

Let $x = .0001; " " 1/x = 10,000$

Let $x = .000001; " " 1/x = 1,000,000$

So, as $x ->0^+ 1/x = oo$

$x->0^-$ means approach from the left side (negative) of zero:
Let $x = -.01; " " 1/x = -100$

Let $x = -.0001; " " 1/x = -10,000$

Let $x = -.000001; " " 1/x = -1,000,000$

So, as $x->0^-$ $1/x = -oo$

How to solve that Limit without graphing ? limx->0^+limx->0^+ 1/x1/x = oooo limx->0^-limx->0^- 1/x1/x -oo-oo