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anonymous

  • one year ago

Find the indicated limit, if it exists.

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  1. anonymous
    • one year ago
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    limx→9f(x),f(x)=[x+927−xx<9x≥9]

  2. anonymous
    • one year ago
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  3. hartnn
    • one year ago
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    have you tried a similar question before ?

  4. anonymous
    • one year ago
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    No.

  5. anonymous
    • one year ago
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    I'm not familiar with matrices in this type of problem

  6. hartnn
    • one year ago
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    Know about left hand and right hand limits?

  7. anonymous
    • one year ago
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    Yeah, I guess

  8. hartnn
    • one year ago
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    so could you find those limits for f(x) ?

  9. anonymous
    • one year ago
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    I don't really know how to do this with matrices.

  10. anonymous
    • one year ago
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    IS the limit 18?

  11. hartnn
    • one year ago
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    its not a matrix :) its a piecewise function, when x<9, f(x) = x+9 when x>= 9, f(x) = 27-x

  12. hartnn
    • one year ago
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    how did you find out that the limit = 18 ?

  13. anonymous
    • one year ago
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    As x approaches nine, f(x) approaches 18. 9+9=18

  14. anonymous
    • one year ago
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    Does that make sense, or am I completely wrong?

  15. hartnn
    • one year ago
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    that makes one-third sense :) let me explain,

  16. anonymous
    • one year ago
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    Gladly.

  17. hartnn
    • one year ago
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    so, we need to find whether x approaches same number when x<9, x=9, x>9 if for all these 3 conditions, f(x) approaches same number, then you limit exist! and the limit value = that number.

  18. hartnn
    • one year ago
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    for x>9, we use x>=9 function which is 27-x so, 27- 9 =18 for x = 9, we use x>=9 again, which is 27-x = 18

  19. anonymous
    • one year ago
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    So the limit does exist?

  20. anonymous
    • one year ago
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    and it is 18

  21. hartnn
    • one year ago
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    for x<9, we use x+9 function so 9+9 = 18 so we indeed get 18 for all 3 conditions! hence limit exist and is = 18 :)

  22. anonymous
    • one year ago
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    Thank you.

  23. hartnn
    • one year ago
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    hope you can try next problem on your own now :) and welcome ^_^

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