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anonymous

  • one year ago

Find the indicated Limit

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  1. anonymous
    • one year ago
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  2. freckles
    • one year ago
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    Have you looked at the left and right limit to x=0?

  3. anonymous
    • one year ago
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    No, I don't understand how this specific example works

  4. freckles
    • one year ago
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    x<0 means to the left of x=0 x>0 means to the right of x=0

  5. freckles
    • one year ago
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    use the functions for x<0 and for x>0 to find the left and right limit

  6. freckles
    • one year ago
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    |dw:1433390979523:dw|

  7. anonymous
    • one year ago
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    Okay, so since there is the x->0 does that mean I use |-4-x| ?

  8. freckles
    • one year ago
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    you use both functions one to find the right limit and one to find the left limit then compare both outputs

  9. freckles
    • one year ago
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    if both outputs are the same then that is what the actual limit is if both outputs are different then the limit does not exist

  10. anonymous
    • one year ago
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    | -4-0 | = 4 5(0) - 8 = -8 correct? so they are different?

  11. freckles
    • one year ago
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    \[\lim_{x \rightarrow 0^-}f(x)=5(0)-8 \text{ here I knew to use } 5x-8 \text{ since we have } x<0 \\ \\ \lim_{x \rightarrow 0^+}f(x)=|-4-0|=4 \text{ I knew to use } |-4-x| \text{ since we have } x>0 \\ \lim_{x \rightarrow 0}f(x) \text{ doesn't exist since left not equal right}\]

  12. freckles
    • one year ago
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    and yes to your question 4 is not -8

  13. anonymous
    • one year ago
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    wow thank you for your help!! for this one, is it 8?

  14. freckles
    • one year ago
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    did you find left and right limit?

  15. freckles
    • one year ago
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    remember we need to look at x->1+ and x->1- x->1+ means look at x>1 x->1- means look at x<1 just as we did before

  16. freckles
    • one year ago
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    except we looked around 0 since we had x approaching 0

  17. anonymous
    • one year ago
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    1-1 = 0 x = 1 = 8 1 + 7 = 8 okay I did them in the order given, but I don't think i did the first one right?

  18. freckles
    • one year ago
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    we are not concerned at what happens at x=1

  19. freckles
    • one year ago
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    \[\lim_{x \rightarrow 1^-}f(x) \\ \text{ this mean we want to know } f(x) \\ \text{ when} x \text{ approaches } 1 \text { from left }\] the function that occurs directly to the left of the vertical line x=1 is f(x)=1-x and we know this because your function tells us to use this function when x<1 so \[\lim_{x \rightarrow 1^-}f(x)=1-1 \] and the the right function to the vertical line x=1 is f(x)=x+7 we know this because your piece-wise function says let's use this function when x>1 \[\lim_{x \rightarrow 1^+}f(x)=1+7\] now it looks like you try to find f(1) which is 8 you wouldn't say x=1=8 because that can't be true but this is unnecessary to the problem

  20. freckles
    • one year ago
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    anyways you can conclude since 0 isn't 8 the limit __________?

  21. anonymous
    • one year ago
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    Oh alright, Yes the limit does not exist

  22. freckles
    • one year ago
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    yep

  23. anonymous
    • one year ago
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    thanks so much, these are just hard for me to understand

  24. freckles
    • one year ago
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    like if you want to explain what is hard about it I can try to explain

  25. freckles
    • one year ago
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    or like what you don't get about what I have said

  26. freckles
    • one year ago
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    when evaluating limits we aren't concerned at what happens at x=a but what happens around x=a

  27. freckles
    • one year ago
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    \[\lim_{x \rightarrow a^-}f(x)\] you see the negative sign that looks like an exponent that tells you want to look directly to the left of x=a and see where the y's are going as x approaches a (From the left)

  28. freckles
    • one year ago
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    |dw:1433392350183:dw|

  29. freckles
    • one year ago
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    |dw:1433392388087:dw| this is where f is to the left of x=a

  30. freckles
    • one year ago
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    notice the y values are approaches k

  31. freckles
    • one year ago
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    |dw:1433392435150:dw|

  32. freckles
    • one year ago
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    that is the left limit of x=a

  33. freckles
    • one year ago
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    now to the right of x=a you want to use the right piece

  34. freckles
    • one year ago
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    |dw:1433392480605:dw|

  35. freckles
    • one year ago
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    those y values are approaching m

  36. freckles
    • one year ago
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    \[\lim_{x \rightarrow a^-}f(x)=k \\ \lim_{x \rightarrow a^+}f(x)=m\]

  37. freckles
    • one year ago
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    |dw:1433392533628:dw| if you wanted to know what the left and right limits of x=b were you will see that they are both c

  38. freckles
    • one year ago
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    |dw:1433392571595:dw| anyways i hope that is more clear

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