## anonymous one year ago Find lim f(x) x-->2

1. anonymous

Do you remember what the definition of a limit is?

2. anonymous

$f(x)\left\{ e^x, x \le2 \right\}\left\{ xe^2, x>2 \right\}$

3. anonymous

the value a graph approaches from both sides.

4. freckles

You must evaluate left and right limit.

5. freckles

Compare both right and left. If they are both equal to L, then the actual limit is L. If they aren't both equal to L, then the limit doesn't exist.

6. anonymous

so how do you figure out what e^x equals

7. freckles

as x approaches 2... well e^x exists and is continuous at x=2 just use direct substitution

8. anonymous

The options are 1, e, e^2, 2e^2, and non existent

9. anonymous

i'm not supposed to use a calculator

10. freckles

I didn't say use a calculator

11. anonymous

so how do you solve e^2 without a calculator

12. freckles

I said to evaluate both left and right limits.. you don't .... it is just e^2 for the left limit $\lim_{x \rightarrow 2^-}f(x)=\lim_{x \rightarrow 2^-}e^x =\lim_{x \rightarrow 2}e^x=e^2 \\ \text{ now also find } \lim_{x \rightarrow 2^+}f(x)=\lim_{x \rightarrow 2^+} x e^{2}=\lim_{x \rightarrow 2} xe^{2}=?$

13. freckles

again just use direct substitution since the function xe^2 is defined and continuous at x=2

14. freckles

I could just say continuous since continuous includes that is defined so xe^2 is continuous at x=2 so you can just use direct sub

15. freckles

@Reid448 are you still there?:

16. anonymous

sorry study hall ended and i had to drive home from school. so the answer is lim f(x) = undefined x-->2

17. anonymous

@freckles

18. freckles

the limit does not exist since left did not equal right that is we know e^2 is not the same as 2*e^2

19. anonymous

ok that makes sense. thx for the help