anonymous
  • anonymous
help find indicated limits
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
@Astrophysics

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anonymous
  • anonymous
@SolomonZelman
SolomonZelman
  • SolomonZelman
\(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5}f(x)}\) where the function is: \(\LARGE\color{black}{ f(x) = \begin{cases} & x+4,~~~{\large x<-5} \\ & 4-x,~~~{\large x\ge-5} \end{cases} }\)
SolomonZelman
  • SolomonZelman
So, for a two-sided limit \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5}f(x)}\) to exist, the limit from the right side and the limit from the left side have to be equal to each other. \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5^+}f(x)=\lim_{x \rightarrow~ -5^-}f(x)}\)
SolomonZelman
  • SolomonZelman
What is our function from the left of -5? (when x is less than -5) it is: x+4 and the function from the right side is 4-x. So this limit: \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5^+}f(x)=\lim_{x \rightarrow~ -5^-}f(x)}\) would go the following way \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5^+}(4-x) =\lim_{x \rightarrow~ -5^-}(x+4) }\)
SolomonZelman
  • SolomonZelman
if both sides are not equivalent to each other, then the two sides limit Does Not Exist (DNE). if both sides are equivalent, then this value they are both equal is going to be your answer.
SolomonZelman
  • SolomonZelman
now, do the substitution directly (plug in -5 for x on both sides)
anonymous
  • anonymous
so it does not exist
anonymous
  • anonymous
what about the other question?
SolomonZelman
  • SolomonZelman
Yes, from the right side the limit is 9 and from the left side the limit is -1. Does Not exist is correct
SolomonZelman
  • SolomonZelman
I need to switch browsers. please wait
SolomonZelman
  • SolomonZelman
I will draw something I can't use on this browser now...
SolomonZelman
  • SolomonZelman
will do without the pic for now
SolomonZelman
  • SolomonZelman
Do you see the part of this (piece wise) function that goes from the right to the point where x=3?
princeharryyy
  • princeharryyy
the function is a broken line at point 3, on x-axis with the lines being with different slope and a point at the top the limit simply doesn't exist.
SolomonZelman
  • SolomonZelman
Em, do you see that segment where the line goes from the right to the point x=3?

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