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anonymous

  • one year ago

Find the indicated limit, if it exists. http://prntscr.com/7ulwx5

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  1. SolomonZelman
    • one year ago
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    for the part of the function that is GREATER than 9, that is: \(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{+}}f(x)\) --------------------------------------------------- for the part of the function that is SMALLER than 9, that is: \(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{-}}f(x)\)

  2. SolomonZelman
    • one year ago
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    If these both limits are equal to each other, then whatever they are both equivalent to, is going to be your answer. If the limit from the left side and the limit from the right side are not equivalent, then your limit DNE

  3. SolomonZelman
    • one year ago
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    If you don't understand what I am saying I can redo the explanation better.

  4. anonymous
    • one year ago
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    ok

  5. anonymous
    • one year ago
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    I understand what you are saying. I just need to know how to find the limit.

  6. SolomonZelman
    • one year ago
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    Just plug in 9 into each of the parts

  7. anonymous
    • one year ago
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    ok so 18 and 18

  8. SolomonZelman
    • one year ago
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    yes, so your answer is 18

  9. anonymous
    • one year ago
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    thanks

  10. SolomonZelman
    • one year ago
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    because the limit from both sides is equal to 18, that means that the two-sided limit is also 18.

  11. anonymous
    • one year ago
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    yes

  12. SolomonZelman
    • one year ago
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    \(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{-}}f(x)=\lim_{x\rightarrow 9}(x+9)=9+9=18\) \(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{+}}f(x)=\lim_{x\rightarrow 9}(27-x)=27-9=18\) Therefore, \(\displaystyle \LARGE\lim_{x\rightarrow 9}f(x)=18\)

  13. SolomonZelman
    • one year ago
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    the 27-x corresponds to the limit from the right side, because it is for greater-than-9 values of x, and x+9 corresponds to the limit from the left side, because it is for smaller-than-9 values of x.

  14. SolomonZelman
    • one year ago
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    You are welcome...

  15. anonymous
    • one year ago
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    That helps a lot. Thank you

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