Mister Exam

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Limit of the function (1+x)/(2-x)

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     /1 + x\
 lim |-----|
x->2+\2 - x/

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)

Limit((1 + x)/(2 - x), x, 2)

Detail solution

Let's take the limit

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)

transform

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)

\lim_{x \to 2^+}\left(- \frac{x + 1}{x - 2}\right) =

False

= -oo

The final answer:

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right) = -\infty

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

Rapid solution [src]

-oo

-\infty

Expand and simplify

One‐sided limits [src]

     /1 + x\
 lim |-----|
x->2+\2 - x/

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)

-oo

-\infty

= -454.0

     /1 + x\
 lim |-----|
x->2-\2 - x/

\lim_{x \to 2^-}\left(\frac{x + 1}{2 - x}\right)

oo

\infty

= 452.0

= 452.0

Other limits x→0, -oo, +oo, 1

\lim_{x \to 2^-}\left(\frac{x + 1}{2 - x}\right) = -\infty

\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right) = -\infty

\lim_{x \to \infty}\left(\frac{x + 1}{2 - x}\right) = -1

\lim_{x \to 0^-}\left(\frac{x + 1}{2 - x}\right) = \frac{1}{2}

\lim_{x \to 0^+}\left(\frac{x + 1}{2 - x}\right) = \frac{1}{2}

\lim_{x \to 1^-}\left(\frac{x + 1}{2 - x}\right) = 2

\lim_{x \to 1^+}\left(\frac{x + 1}{2 - x}\right) = 2

\lim_{x \to -\infty}\left(\frac{x + 1}{2 - x}\right) = -1

Numerical answer [src]

-454.0

-454.0

The graph