## askme12345 5 years ago How to find the equation and limits?

of 5/x-2 and y=x+4/x^2+9

question states: find the horizontal or oblique asymptotes and write their equation and also state in limit form

3. anonymous

To find the horizontal asymptote you have to take the limit of the function at +- $\infty$

4. anonymous

Because the idea is that as the function approaches +- infinity it approaches a certain y value.

can you explain how to so that with 5/x-2

6. anonymous

I'm not sure what you're asking. Is 5 / (x-2) = f(x)?

7. anonymous

If that was the case, you would write the problem like this: lim 5/(x-2) = x(5/x / 1 -2/x/1) = 0 x->$\infty$

8. anonymous

Because as x approaches infinity, the denominator gets bigger and bigger causing the y value to get smaller and smaller (when you divide a number by a larger number it makes it smaller). Therefore, it would be the same for negative infinity. So you have a horizontal asymptote at y = 0