Question

Find the vertical asymptote of f(x) 1/x^2

Answer 1

It's no finite because for a vertical asymptote you must factor the denominator. since x^2 does not factor out, the limit dne

Answer 2

Oh, I get it now, that's why i wouldn't get a reasonable answer, thank you.

Answer 3

plug in a huge number for x

Answer 4

should be zero i think

Answer 5

The question asks for the asymptote.

Answer 6

at zero.

Answer 7

That's when the denominator vanishes.

Answer 8

But it says if any.

Answer 9

Find the asymptote (if any).

Answer 10

If the denominator is always positive, such as f(x)=1/(x^2+1), then there is no vertical asymptote.

Answer 11

Do you know where the denominator vanishes?

Answer 12

@meylispena "where" means x=?

Answer 13

retricemptote is at 0

Answer 14

the denominator can't be zero and if it vanishes... then the asymptote DNE

Answer 15

It doesn't give you a graph or anything else, just to find the asymptote if any of f(x) 1/x^2

Answer 16

@swin2013 the limit of f(x) at x=0 does not exist, but that doesn't mean that there is no vertical asymptote.

Answer 17

x would equal 0.

Answer 18

That's what I believe.

Answer 19

@meylispena The purpose of the exercise is to identify the vertical asymptote without plotting the graph of the function.
Can you explain why?

Answer 20

My book has answers in the back, I shall check what the answer is.

Answer 21

A vertical asymptote must be factored out in the denominator. Since there is not factors, there is no finite limit. It's like dividing a constant with a number that is getting smaller. The limit is approaching infinity.

Answer 22

It doesn't give you a graph or anything else, just to find the asymptote if any of f(x) 1/x^2

1/x^2 is a function you can graph it paste it to google and you'll see asymptote is at zero.

Answer 23

The answer is correct, but it is more important to know why so that you can do other problems.

Answer 24

My book says x = 0 but I don't really understand why and that's what I have to show.

Answer 25

@meylispena
When the denominator vanishes (=0), the function does not exist at that point, as the value tends to infinity when x->0.
But when x is very small (but not equal to zero), the function is defined and has a very large value. That is why it is called vertical asymptote.

Answer 26

Oh, I understand it now. Thank you.

Answer 27

You're very welcome! :)

Answer 28

(: