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anonymous

  • one year ago

Find lim f(x) x-->2

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  1. anonymous
    • one year ago
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    Do you remember what the definition of a limit is?

  2. anonymous
    • one year ago
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    \[f(x)\left\{ e^x, x \le2 \right\}\left\{ xe^2, x>2 \right\}\]

  3. anonymous
    • one year ago
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    the value a graph approaches from both sides.

  4. freckles
    • one year ago
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    You must evaluate left and right limit.

  5. freckles
    • one year ago
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    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
    • one year ago
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    so how do you figure out what e^x equals

  7. freckles
    • one year ago
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    as x approaches 2... well e^x exists and is continuous at x=2 just use direct substitution

  8. anonymous
    • one year ago
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    The options are 1, e, e^2, 2e^2, and non existent

  9. anonymous
    • one year ago
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    i'm not supposed to use a calculator

  10. freckles
    • one year ago
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    I didn't say use a calculator

  11. anonymous
    • one year ago
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    so how do you solve e^2 without a calculator

  12. freckles
    • one year ago
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    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
    • one year ago
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    again just use direct substitution since the function xe^2 is defined and continuous at x=2

  14. freckles
    • one year ago
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    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
    • one year ago
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    @Reid448 are you still there?:

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

  17. anonymous
    • one year ago
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    @freckles

  18. freckles
    • one year ago
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    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
    • one year ago
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    ok that makes sense. thx for the help

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