## Amenah8 one year ago LIMITS: Click to see question

1. Amenah8

$\lim_{x \rightarrow \pm \infty} (x^4+x^3)/(12x^3+128)$

2. freckles

divide top and bottom by x^3

3. freckles

we are dividing top and bottom by x^3 because the degree of the bottom polynomial is 3

4. freckles

$\lim_{x \rightarrow \infty} \frac{\frac{x^4}{x^3}+\frac{x^3}{x^3}}{\frac{12x^3}{x^3}+\frac{128}{x^3}}$

5. freckles

now figure out the limit for each of those mini-fractions

6. Amenah8

oh!i remember how to do this! one moment while i work it out, please?

7. Amenah8

$(x+1)/(12+128/x^3)$

8. Amenah8

and then replace x with 0, right?

9. Amenah8

i mean with infinity

10. freckles

right now you must look at x approaches infinity and also x approaches -negative infinity

11. Amenah8

$\infty+1/12+0$ ?

12. freckles

so you have infinity for x approaches infinity ok now you need to evaluate your second question which involves x going to -infinity

13. Amenah8

ok, one moment

14. Amenah8

$-\infty+1/12+0$ ?

15. freckles

right so you have: $\lim_{x \rightarrow \infty}\frac{x+1}{12+\frac{128}{x^3}} =\frac{\infty}{12+0}=\infty \\ \lim_{x \rightarrow -\infty} \frac{x+1}{12+\frac{128}{x^3}}=\frac{-\infty}{12+0}=-\infty$

16. freckles

also I like to separate my numerators by doing ( ) and my denominators by doing ( ) like I would write what you said like (-infty+1)/(12+0) it is more proper and correct :p

17. Amenah8

haha, okay! thank you so much!

18. freckles

np