anonymous
  • anonymous
Find the indicated limit, if it exists. http://prntscr.com/7ulwx5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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SolomonZelman
  • SolomonZelman
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: \(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{-}}f(x)\)
SolomonZelman
  • SolomonZelman
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
SolomonZelman
  • SolomonZelman
If you don't understand what I am saying I can redo the explanation better.

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anonymous
  • anonymous
ok
anonymous
  • anonymous
I understand what you are saying. I just need to know how to find the limit.
SolomonZelman
  • SolomonZelman
Just plug in 9 into each of the parts
anonymous
  • anonymous
ok so 18 and 18
SolomonZelman
  • SolomonZelman
yes, so your answer is 18
anonymous
  • anonymous
thanks
SolomonZelman
  • SolomonZelman
because the limit from both sides is equal to 18, that means that the two-sided limit is also 18.
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
\(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{-}}f(x)=\lim_{x\rightarrow 9}(x+9)=9+9=18\) \(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{+}}f(x)=\lim_{x\rightarrow 9}(27-x)=27-9=18\) Therefore, \(\displaystyle \LARGE\lim_{x\rightarrow 9}f(x)=18\)
SolomonZelman
  • SolomonZelman
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.
SolomonZelman
  • SolomonZelman
You are welcome...
anonymous
  • anonymous
That helps a lot. Thank you

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