## Dodo1 Group Title How do you find horizontal asymptote ? one year ago one year ago

1. ash2326 Group Title

Suppose you have a function $y=f(x)$ Express x in terms of y, now find value of y for which x goes to infinity or - infinity That value of y is your horizontal asymptote

2. pottersheep Group Title

This website helped me a lot when I was learning about horizontal aymptotes. http://www.purplemath.com/modules/asymtote2.htm

3. pottersheep Group Title

Btw, your line CAN touch a horizontal aymptote. "Whereas vertical asymptotes are sacred ground, horizontal asymptotes are just useful suggestions. Whereas you can never touch a vertical asymptote, you can (and often do) touch and even cross horizontal asymptotes. Whereas vertical asymptotes indicate very specific behavior (on the graph), usually close to the origin, horizontal asymptotes indicate general behavior far off to the sides of the graph. "

4. ash2326 Group Title

@Dodo1 do you understand?

5. Dodo1 Group Title

This is a question A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. Show that each of the following functions has a horizontal asymptote by calculating the given limit. $\lim_{x \rightarrow \infty}10+\frac{ 3x }{ x^2-12x+3 }$

6. Dodo1 Group Title

Yes, the basic concept! thank you i will take note.

7. pottersheep Group Title

Let me get my grade 12 notes

8. pottersheep Group Title

If y = [ax^n + ...............]/[Ax^N +.................] the horizontal asymptote = 0

9. pottersheep Group Title

Is the exponent on the bottom is greater than the one on the top, then it approaches zero

10. ash2326 Group Title

Yes this is a way too, let's find the limit here $\lim_{x \rightarrow \infty}10+\frac{ 3x }{ x^2-12x+3 }$ Can you find the limit?

11. pottersheep Group Title

Because eventually, the number on the bottom will become HUGEEEEE compared to the top. And a number / a hugeeeeeeeee number is close to zero, a veryy small decimal!

12. pottersheep Group Title

That's how I understood it :)

13. Dodo1 Group Title

ok, thsnk you potterssheep. :) how do i find limit?

14. ash2326 Group Title

$\lim_{x \rightarrow \infty}10+\frac{ 3x }{ x^2-12x+3 }$ First divide the numerator and denominator by x $\lim_{x \rightarrow \infty}10+\frac{ 3\frac x x }{ \frac{x^2}{x}-12\frac x x +\frac 3 x}$ We'll get $\lim_{x\to \infty} 10+\frac 3 {x-12+\frac 3 x }$ 3/x =0 so we get $\lim_{x\to \infty} 10+\frac 3 {x-12}$ as $$x\to \infty$$ we get \$10+\frac 3 \infty$ $=10+0=>10$ so that's the limit

15. Dodo1 Group Title

I see but why x-12= infinity?

16. ash2326 Group Title

$x-12$ $\infty-12$ Infinity is a very big no. subtracting 12 won't change it $\infty-12 \longrightarrow \infty$

17. Dodo1 Group Title

Oh i see thank you!! how about $\lim_{x \rightarrow -\infty} \frac{ 5-8x }{ 7+x }+\frac{ (6x^2+8) }{ (14x-12)^2 }$

18. Dodo1 Group Title

Do I mutliply the ()2 first then add?

19. ash2326 Group Title

$\lim_{x \rightarrow -\infty} \frac{ 5-8x }{ 7+x }+\frac{ (6x^2+8) }{ (14x-12)^2 }$ Let's split the limits $\lim_{x \rightarrow -\infty} \frac{ 5-8x }{ 7+x }$ First step divide by x , numerator and denominator $\lim_{x \rightarrow -\infty} \frac{\frac 5 x -8}{\frac 7 x +1}$ 1/x terms will become 0, when x goes to + or - infinity. We'll get $\frac{-8}{1}$ Do you get this?

20. Dodo1 Group Title

OK, i got it so far.

21. Dodo1 Group Title

:) its fun!

22. ash2326 Group Title

Great, now the second part $\lim_{x \rightarrow -\infty}\frac{ (6x^2+8) }{ (14x-12)^2 }$ Let's expand the denominator $\lim_{x \rightarrow -\infty}\frac{ (6x^2+8) }{ (196x^2-336x+144) }$ Divide numerator and denominator by x^2, $\lim_{x \rightarrow -\infty}\frac{ (6+\frac8{x^2}) }{ (196-336\frac{x}{x^2}+\frac{144}{x^2}) }$Can you find the limit from here?

23. Dodo1 Group Title

mmm, 6/(196-336)?

24. ash2326 Group Title

x/x^2=1/x $x\to -\infty$$\frac 1 x \to 0, \frac 1 {x^2} \to 0$

25. ash2326 Group Title

Try again now :)

26. Dodo1 Group Title

6/196?

27. ash2326 Group Title

yes, limit is the combined limit

28. Dodo1 Group Title

whats combined limit?

29. ash2326 Group Title

$-8+\frac 6 {196}$

30. Dodo1 Group Title

Oh i see! - infinity and infinity are really matter? beacuse it seems that it does nt matter.?

31. ash2326 Group Title

It does matter, in this question it doesn't

32. Dodo1 Group Title

oh, not horizentally matter?

33. ash2326 Group Title

nope

34. Dodo1 Group Title

got it! thank you, i have other 4 questions but i will try and if i stuck can i ask you?

35. ash2326 Group Title

Okay, try them. If I'm here, I'll help you But ask them in a new question. Close this