## dainel40 2 years ago Find the limit of this look at the attached file

1. dainel40

2. dainel40

3. dainel40

@jim_thompson5910 they said u could help

4. dainel40

I think the answer does not Exist

5. jim_thompson5910

using the limit laws, we can say $\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))$ $\Large \lim_{x\to 2}x^3 f(x) = 2^3 * f(2)$ $\Large \lim_{x\to 2}x^3 f(x) = 8 * f(2)$ $\Large \lim_{x\to 2}x^3 f(x) = ???$

6. jim_thompson5910

to find f(2) you would either use a function or the graph since you don't have the function, you'll have to use the graph

7. dainel40

but the graph has a hole and a solution thats where im confused

8. dainel40

at x->2

9. jim_thompson5910

ok as x gets closer and closer to 2, the graph is approaching the point (2,2) sure there is a hole here, but if you start on either side of x = 2 and approach it, you'll reach this hole so that's why $\Large \lim_{x\to 2} f(x) = 2$

10. jim_thompson5910

$\Large \lim_{x\to 2}x^3 f(x) = (\lim_{x\to 2}x^3) * (\lim_{x\to 2}f(x))$ $\Large \lim_{x\to 2}x^3 f(x) = 2^3 * 2$ $\Large \lim_{x\to 2}x^3 f(x) = 8 * 2$ $\Large \lim_{x\to 2}x^3 f(x) = 16$

11. dainel40

oh... I see.. Thanks a lot! I have another question.. Could I ask you?

12. jim_thompson5910

sure go for it

13. dainel40

If f and g are continuous functions with f(1) = 5 and the following limit, find g(1).

14. dainel40

im getting 8 as a result not sure

15. jim_thompson5910

this is a completely different problem right (with different functions f and g)?

16. jim_thompson5910

oh wait nvm

17. dainel40

yes

18. jim_thompson5910

that's correct, g(1) = 8

19. jim_thompson5910

you separate the limit up plug in x = 1 then replace f(1) with 5 and g(1) with y afterwards you solve for y to get y = 8

20. dainel40

yay! Thank You so much for your help!

21. jim_thompson5910

you're welcome