Find the limit ?

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2 Answers
Mar 18, 2017

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,

Mar 18, 2017

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