## cassieforlife5 one year ago find the limit as f(g(x)) approaches 1 f(x)= 3/(x-1) g(x)= x^4 I got f(g(x))= 3/(x^4-1) but I need help finding the limit.

1. anonymous

There's a vertical asymptote at 1. Have you tried taking the limits from the left and right sides?

2. cassieforlife5

on my graph I don't see a left hand limit, but is the right hand limit infinity?

3. anonymous

Yes the right is infinity Does your graph look like this?|dw:1442790635351:dw|

4. cassieforlife5

yes wait then from the left isn't the limit negative infinity

5. anonymous

right

6. anonymous

since the left and right limits aren't the same, the limit does not exist

7. cassieforlife5

ohhhh i see. Thanks so much! If you have time, would you mind helping me with another limit question? I'm not very good at limits

8. anonymous

sure

9. cassieforlife5

find the limit as x approaches 0 of (3x^4 - 6x^3)/(4x^3 + 2x^2)

10. anonymous

I'd start this one by factoring to see what cancels out.

11. cassieforlife5

okay so I got 3x^3(x-2) / 2x^2(2x+1)

12. anonymous

right, and two of the x's in the numerator will cancel the x² in the denominator, and then you can plug in the 0

13. anonymous

$\frac{3x(x-2)}{2(2x+1)}$

14. cassieforlife5

I got 0 as my answer

15. anonymous

that's right :)

16. cassieforlife5

Thanks a million! You're really a lifesaver!! :D

17. anonymous

you're welcome