## calculus130 Group Title calculate, if existent, via l'Hopital rule: lim-->3 x^2+x-12/x^3-x^2-6x one year ago one year ago

1. infoshark Group Title

what do you get when u sub in 3 ?

2. calculus130 Group Title

i am clueless totally..

3. infoshark Group Title

if you put 3 instead of x, what do you get ?

4. calculus130 Group Title

12/0

5. calculus130 Group Title

i get 12/0

6. infoshark Group Title

try one more time.

7. calculus130 Group Title

oh yeah 0/0

8. infoshark Group Title

now u can use l'hopital's rule. do the derivative of the top over the derivative of the bottom

9. calculus130 Group Title

i have done it that way too but i need step by step to check my answer

10. infoshark Group Title

whats the derivative of the numerator over the derivative of the denom that you got ?

11. calculus130 Group Title

2/6x-2

12. infoshark Group Title

2x+1 / 3x^2-2x-6

13. infoshark Group Title

plug in 3 for x.

14. calculus130 Group Title

if i plug 3 for x then the final answer is 7/9 is that right?

15. richyw Group Title

$\lim_{x\rightarrow 3} \frac{ x^2+x-12}{x^3-x^2-6x}$Plug in and see we have an indeterminate form.$\frac{ 3^2+3-12}{3^3-3^2-6(3)}=\frac{0}{0}$Appling L'Hopitals rule$\lim_{x\rightarrow 3} \frac{ \frac{d}{dx}(x^2+x-12)}{\frac{d}{dx}(x^3-x^2-6x)}$$\lim_{x\rightarrow 3} \frac{ 2x+1}{3x^2-2x-6}$$\frac{2(3)+1}{3(3)^2-2(3)-6}$$\frac{6+1}{27-6-6}=\frac{7}{15}$

16. calculus130 Group Title

thanks you so much my friend

17. richyw Group Title

for future reference, if you are just checking your answers, see if wolfram will give you the steps first... http://www.wolframalpha.com/input/?i=lim+x-%3E3+%28x%5E2%2Bx-12%29%2F%28x%5E3-x%5E2-6x%29

18. calculus130 Group Title

thank you again for the link