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Limit of the function/ 1/(1-x)

Limit of the function 1/(1-x)

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       1  
 lim -----
x->oo1 - x

\lim_{x \to \infty} \frac{1}{1 - x}

Limit(1/(1 - x), x, oo, dir='-')

Detail solution

Let's take the limit

\lim_{x \to \infty} \frac{1}{1 - x}

Let's divide numerator and denominator by x:

\lim_{x \to \infty} \frac{1}{1 - x}

\lim_{x \to \infty}\left(\frac{1}{x \left(-1 + \frac{1}{x}\right)}\right)

Do Replacement

u = \frac{1}{x}

then

\lim_{x \to \infty}\left(\frac{1}{x \left(-1 + \frac{1}{x}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u}{u - 1}\right)

\frac{0}{-1} = 0

The final answer:

\lim_{x \to \infty} \frac{1}{1 - x} = 0

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

Plot the graph

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} \frac{1}{1 - x} = 0

\lim_{x \to 0^-} \frac{1}{1 - x} = 1

\lim_{x \to 0^+} \frac{1}{1 - x} = 1

\lim_{x \to 1^-} \frac{1}{1 - x} = \infty

\lim_{x \to 1^+} \frac{1}{1 - x} = -\infty

\lim_{x \to -\infty} \frac{1}{1 - x} = 0

Rapid solution [src]

0

Expand and simplify

The graph