Question

Find the limit if it exist

Answer 1

\[\lim_{x \rightarrow \infty}\frac{ 5+3x-x^2 }{ 4x^2-25 }\]

Answer 2

consider -1x^2/4x^2 =-1/4

Answer 3

There is a break of the continuous graph in both x = 2.5 and x = -2.5

This can be solved looking at the denominator

4x^2-25
(2x-5)(2x+5)

Now solve for 0

2x-5 = 0

2.5 = x

2x+5 = 0

-2.5 = x

Answer 4

Does that make sense?

Answer 5

nope

Answer 6

denominator = 0 is not a limit though, that is when the equation is undefined

Answer 7

Correct. But it does show where the limit of the graph is. When the graph approaches -2.5 and 2.5, it will reach to -infinity and +infinity. From the information you will be able to see the limits of it.