Question

Lim x->-5(((1)/(5)+(1)/(x))/(10+2x))=correct answer 1/10x = -1/50explain:

Answer 1

Given:

The limit problem is:

$lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}$

To find:

The value of the given limit problem.

Solution:

We have,

$lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}$

It can be written as:

$=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}$

$=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}$

$=lim_{x\to -5}\dfrac{1}{5x\times 2}$

$=lim_{x\to -5}\dfrac{1}{10x}$

Applying limit, we get

$lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}$

$lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}$

Therefore, the value of given limit problem is $-\dfrac{1}{50}$.