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anonymous

  • one year ago

help find indicated limits

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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  3. anonymous
    • one year ago
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    @Astrophysics

  4. anonymous
    • one year ago
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    @SolomonZelman

  5. SolomonZelman
    • one year ago
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    \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5}f(x)}\) where the function is: \(\LARGE\color{black}{ f(x) = \begin{cases} & x+4,~~~{\large x<-5} \\ & 4-x,~~~{\large x\ge-5} \end{cases} }\)

  6. SolomonZelman
    • one year ago
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    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. \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5^+}f(x)=\lim_{x \rightarrow~ -5^-}f(x)}\)

  7. SolomonZelman
    • one year ago
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    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 \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ -5^+}(4-x) =\lim_{x \rightarrow~ -5^-}(x+4) }\)

  8. SolomonZelman
    • one year ago
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    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.

  9. SolomonZelman
    • one year ago
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    now, do the substitution directly (plug in -5 for x on both sides)

  10. anonymous
    • one year ago
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    so it does not exist

  11. anonymous
    • one year ago
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    what about the other question?

  12. SolomonZelman
    • one year ago
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    Yes, from the right side the limit is 9 and from the left side the limit is -1. Does Not exist is correct

  13. SolomonZelman
    • one year ago
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    I need to switch browsers. please wait

  14. SolomonZelman
    • one year ago
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    I will draw something I can't use on this browser now...

  15. SolomonZelman
    • one year ago
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    will do without the pic for now

  16. SolomonZelman
    • one year ago
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    Do you see the part of this (piece wise) function that goes from the right to the point where x=3?

  17. princeharryyy
    • one year ago
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    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.

  18. SolomonZelman
    • one year ago
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    Em, do you see that segment where the line goes from the right to the point x=3?

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