Find the limit ?

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2 Answers
Gió · Anjali G
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,

Anjali G
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

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