## clara1223 one year ago find the limit as x approaches infinity of (4x-7)/((5x^2)+3x+7)

1. clara1223

$\lim_{x \rightarrow \infty}\frac{ 4x-7 }{ 5x ^{2}+3x+7 }$

2. clara1223

We haven't gone over limits as x approaches infinity in class before.

3. amistre64

divide it all by the highest power of x to simplify. anything left with an x in the denominator will zero out since 1/inf is a very very small amount of cake to get

4. clara1223

so multiply the denominator by 1/x^2?

5. amistre64

your basically searching for any horizontal asymptotes ... you covered them yet?

6. amistre64

top and bottom yes

7. amistre64

there are 'rules' which you can commit to memory if you have the gigabytes to play with :)

8. clara1223

so I'm left with $\frac{ \frac{ 4 }{ x }-\frac{ 7 }{ x ^{2} } }{ 5+\frac{ 3 }{ x }+\frac{ 7 }{ x ^{2} } }$

9. amistre64

now everything with an x under it, goes to something very very small, they approach zero. what are we left with?

10. clara1223

1/5?

11. amistre64

powers of x that is ... 4/x - 7/x^2 is not 1

12. clara1223

-1?

13. amistre64

0-0 = ??

14. clara1223

oh so the answer is 0?

15. amistre64

yep

16. clara1223

because 0/5=0

17. amistre64

one rule, if the bottom is a higher degree than the top, as x approaches infinity, the limit is zero

18. amistre64

if they are of the same degree, they limit to their leading coeffs .. its just simpler to divide off by the highest power of x and assess