## El_Arrow one year ago need help with limit problem

1. El_Arrow

2. El_Arrow

okay so my question is why is it dividing by n?

3. El_Arrow

i thought you divided by the value with the largest power

4. Melodious

guys pls help me out in my question

5. El_Arrow

@amistre64

6. El_Arrow

@IrishBoy123

7. ganeshie8

Next you should be asking why is it dividing by the term with largest power

8. El_Arrow

i dont understand

9. ganeshie8

Notice that "n" is indeed the largest power in the denominator, but clearly you're missing the key point, dividing by "n" is not really necessary here

10. ganeshie8

Look at the expression $\dfrac{n^3}{n+8}$ what happens to this term as "n" becomes large ? which one grows faster, numerator or denominator ?

11. El_Arrow

the denominator

12. ganeshie8

are you saying "n+8" grows faster than "n^3" ?

13. ganeshie8

plugin n=10, 100 etc and see which one is growing faster

14. El_Arrow

no i meant the numerator

15. ganeshie8

Okay what about the value of expression as "n" gets large ?

16. El_Arrow

it goes to infinity right

17. ganeshie8

|dw:1436635975751:dw|

18. ganeshie8

As you can see the function f(x) = x^3/(x+8) is increasing without any bound as x increases, so the corresponding sequence diverges

19. ganeshie8

They are dividing top and bottom by "n" so that it becomes easy for you to see the same

20. ganeshie8

$a_n = \dfrac{n^3}{n+8} = \dfrac{n^2}{1+8/n}$ "plugin" $$n = \infty$$, the expression becomes $\dfrac{\infty^2}{1+8/\infty} = \dfrac{\infty^2}{1+0} = \infty$

21. El_Arrow

i think i understand better now

22. ganeshie8

In general : For any rational function, $$f(x) = \dfrac{P(x)}{Q(x)}$$ , as $$x\to\infty$$, we have $$f(x)\to\pm\infty$$ if the degree of $$P(x)$$ is greater than the degree of $$Q(x)$$