Question

Find the limit ?

Answer 1

I would say that it tends to `+oo` from the left and `-oo` from the right, or the limit diverges.

Explanation:

If you use `x=-5` into your function you get:
`(25+35+10)/(25-25)=70/0`
this tells us that as `x->-5` our function will become very big, so our limit would tend to `+-oo` depending upon the side you are considering:
Graphically:
graph{(x^2-7x+10)/(x^2-25) [-12.66, 12.65, -6.33, 6.33]}
as you can see at `x=-5` you have a discontinuity,

Answer 2

`lim_(x->-5)(frac{x^2-7x+10}{x^2-25})" does not exist"`

Explanation:

`lim_(x->-5)(frac{x^2-7x+10}{x^2-25})`

Use direct substitution:
`frac{(-5)^2-7(-5)+10}{(-5)^2-25}=70/0`

Thus, the limit does not exist because `70/0` is undefined.

Check with a graph:
graph{(x^2-7x+10)/(x^2-25) [-12.66, 12.65, -6.33, 6.33]}
As you can see, at `x=-5`, the function approaches `oo` from the left and `-oo` from the right.

*Note: We cannot use L'Hospital's rule because `70/0` is not an indeterminate case