## DLS 2 years ago Limits

1. DLS

$\lim_{x \rightarrow \infty }\frac{x^4+2x^3+3}{2x^4-x+2}$

2. DLS

x+1 is a factor of this right?

3. DLS

however,no use..

4. TomLikesPhysics

I think it is one half. Because you got up- and downstairs and x^4 which I think is a special case and in which the limit approaches the coefficents before these two identical powers of x which is 1upstairs and 2 downstairs - 1/2.

5. DLS

it is 1/2 only but how

6. TomLikesPhysics

If you would use the L`Hopital Rule you would end up with it.

7. TomLikesPhysics

Do you want to see the calculation?

8. DLS

$\lim_{x \rightarrow \infty }\frac{3x^4+4x^3+}{4x^4+x^2+7}$ I'm trying to do this with the same concept but i'm getting 5/7 @TomLikesPhysics ?

9. DLS

+5

10. DLS

*

11. DLS

$\frac{12x^3+12x^2}{16x^3+2x}$

12. TomLikesPhysics

should be 3/4

13. DLS

??

14. TomLikesPhysics

the one where you got 5/7

15. DLS

okay got it!

16. DLS

but how is it gaining infinity/infinity?

17. TomLikesPhysics

How it gains infinity? You take the limit where x goes to infinity. So both terms grow. Is that what you meant?

18. DLS

it is something+infinity is it samething?

19. DLS

$\lim_{x \rightarrow \infty } \frac{x^3+x^2+4}{x^2+8}$ are you gettng 1 here?

20. TomLikesPhysics

Here it should be infinity. You got downstairs an x^2 and upstairs and x^3. So the x^3 "is stronger" and wins and therefore the whole thing goes to infinity.

21. DLS

No,I solved according to what you said and got this: $\frac{3x^2+2x}{2x}$ so I got 3x+1=1?

22. TomLikesPhysics

How do you end up with 3x+1=1 if you got a fraction?

23. DLS

$\frac{3x^2}{2x} + \frac{2x}{2x}$

24. DLS

I ended up with: $\frac{3}{2}x+1$

25. TomLikesPhysics

k but if you got 3x+1 and let x approach infinity (taking the limit) than you end up with infinity.

26. DLS

okay! if it was 1/x and x==> infinity it would have been 1 RIGHT?

27. TomLikesPhysics

limit x-> inf. of ax+b is alsways infinity. The b does not matter in the long run and nether does a while x gets bigger and bigger.

28. DLS

Great.Clear now :)

29. TomLikesPhysics

If you got 1/x and x gets bigger and bigger you would get a limit which is 0.

30. DLS

yeah!

31. TomLikesPhysics

1/x as x approaches infinity is 0. 1/x as x approaches 0 is infinity.

32. DLS

$\lim_{x \rightarrow 0} \frac{\cos7x-\cos9x}{\cos3x-\cos5x}$ These ones?

33. TomLikesPhysics

I don´t know. Have not seen this one before.^^ Never dealt with limits and sine or cosine.

34. DLS

okay..book did a direct step after this :| $\frac{2\sin8xsinx}{2\sin4xsinx}$

35. TomLikesPhysics

^^ First time I see that kind of stuff. I´m sorry but with that I can not help you.