Question

Find lim f(x)
x-->2

Answer 1

Do you remember what the definition of a limit is?

Answer 2

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

Answer 3

the value a graph approaches from both sides.

Answer 4

You must evaluate left and right limit.

Answer 5

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.

Answer 6

so how do you figure out what e^x equals

Answer 7

as x approaches 2...

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

Answer 8

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

Answer 9

i'm not supposed to use a calculator

Answer 10

I didn't say use a calculator

Answer 11

so how do you solve e^2 without a calculator

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

@Reid448 are you still there?:

Answer 16

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

Answer 17

@freckles

Answer 18

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

Answer 19

ok that makes sense. thx for the help