limit as x approaches 1+ of 1/(x-1) — step-by-step solution

Let's evaluate the limit of

\frac{1}{x - 1}

when

x \to 1

⁺

ⓘ The limit of a sum of finite limits is the sum of the limits

The limit of

x - 1

is (

1 - 1

)⁺ when

x \to 1

⁺

⇥Let's calculate:

1 - 1

⇥ⓘ Start from

1

and move back

1

on the number line, down to zero:

1 - 1

0

⇥

0

ⓘ A nonzero number divided by a quantity that tends to 0 grows without bound, the signs giving +∞ or -∞

So the limit of

\frac{1}{x - 1}

+∞

when

x \to 1

⁺

▶Limit:

+∞