Question

Lim x->-5(((1)/(5)+(1)/(x))/(10+2x))=

correct answer 1/10x = -1/50

explain:

Answer 1

Given:

The limit problem is:

`lim_(x\to -5)((1)/(5)+(1)/(x))/(10+2x)`

To find:

The value of the given limit problem.

Solution:

We have,

`lim_(x\to -5)((1)/(5)+(1)/(x))/(10+2x)`

It can be written as:

`=lim_(x\to -5)((x+5)/(5x))/(2(5+x))`

`=lim_(x\to -5)(x+5)/(5x)* (1)/(2(5+x))`

`=lim_(x\to -5)(1)/(5x* 2)`

`=lim_(x\to -5)(1)/(10x)`

Applying limit, we get

`lim_(x\to -5)(1)/(10x)=(1)/(10(-5))`

`lim_(x\to -5)(1)/(10x)=(1)/(-50)`

Therefore, the value of given limit problem is
`-(1)/(50)`.