anonymous
  • anonymous
Find lim f(x) x-->2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Do you remember what the definition of a limit is?
anonymous
  • anonymous
\[f(x)\left\{ e^x, x \le2 \right\}\left\{ xe^2, x>2 \right\}\]
anonymous
  • anonymous
the value a graph approaches from both sides.

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More answers

freckles
  • freckles
You must evaluate left and right limit.
freckles
  • 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.
anonymous
  • anonymous
so how do you figure out what e^x equals
freckles
  • freckles
as x approaches 2... well e^x exists and is continuous at x=2 just use direct substitution
anonymous
  • anonymous
The options are 1, e, e^2, 2e^2, and non existent
anonymous
  • anonymous
i'm not supposed to use a calculator
freckles
  • freckles
I didn't say use a calculator
anonymous
  • anonymous
so how do you solve e^2 without a calculator
freckles
  • freckles
I said to evaluate both left and right limits.. you don't .... it is just e^2 for the left limit \[\lim_{x \rightarrow 2^-}f(x)=\lim_{x \rightarrow 2^-}e^x =\lim_{x \rightarrow 2}e^x=e^2 \\ \text{ now also find } \lim_{x \rightarrow 2^+}f(x)=\lim_{x \rightarrow 2^+} x e^{2}=\lim_{x \rightarrow 2} xe^{2}=?\]
freckles
  • freckles
again just use direct substitution since the function xe^2 is defined and continuous at x=2
freckles
  • 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
freckles
  • freckles
@Reid448 are you still there?:
anonymous
  • anonymous
sorry study hall ended and i had to drive home from school. so the answer is lim f(x) = undefined x-->2
anonymous
  • anonymous
@freckles
freckles
  • 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
anonymous
  • anonymous
ok that makes sense. thx for the help

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