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haterofmath

  • 2 years ago

find the indicated one-sided limit. if the limiting value is inifinte indicate whther is is +∞or− , lim x→4 (3x−9)

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  1. hsmt
    • 2 years ago
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    hi. i have a question. is the limit being taken from the left or right?

  2. hsmt
    • 2 years ago
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    are you there?

  3. hsmt
    • 2 years ago
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    well, this is a linear function or a first degree polynomial.

  4. haterofmath
    • 2 years ago
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    i'm not sure

  5. hsmt
    • 2 years ago
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    so tell me what the problem is asking, if you would be so kind.

  6. haterofmath
    • 2 years ago
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    \[\lim_{x \rightarrow 4}(3x^2-9) \]

  7. hsmt
    • 2 years ago
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    can you tell me in words, what it is asking?

  8. haterofmath
    • 2 years ago
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    find the indicated one-sided limit. if the limiting value is inifinte, indicate whether it is \[+\infty or -\]

  9. haterofmath
    • 2 years ago
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    -infity

  10. hsmt
    • 2 years ago
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    ok. so they want the limit of 3x^2-9 as x approaches 4. I see the 4, but is it a left- or right hand + limit. My glasses may not be picking up the detail.

  11. haterofmath
    • 2 years ago
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    right hand

  12. hsmt
    • 2 years ago
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    ok. perfect. now, what do we know about 3x^2-9? what kind of a function is it?

  13. hsmt
    • 2 years ago
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    what is the graph of that function?

  14. haterofmath
    • 2 years ago
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    i'm not sure...i'm a little confused on the whole topic of limits

  15. hsmt
    • 2 years ago
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    it is ok. it is a second degree polynomial. i am stating it this way because there is a limit theorem that states that all polynomial functions are continuous and all polynomial functions have equal left and right hand limits at every point in their domain.

  16. hsmt
    • 2 years ago
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    this function would graph out to be a parabola. Furthermore, unless special domains are part of the problem, you simply substitute the x value into the expression to get the limit.

  17. haterofmath
    • 2 years ago
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    oh ok

  18. hsmt
    • 2 years ago
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    incidentally, polynomial functions are any function that can be written in the form: y=ax^n+bx^(n-1)+...+c

  19. hsmt
    • 2 years ago
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    so, 5x^6+3x^5+4=y is a sixth degree polynomial function. notice the degree and the highest power are the same.

  20. haterofmath
    • 2 years ago
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    yea

  21. hsmt
    • 2 years ago
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    ok. the only reason i bring this up is because they tend to throw a lot of these polynomial functions at you in calc classes. now back to the problem at hand. did you substitute 4 for x in the expression?

  22. hsmt
    • 2 years ago
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    if so, what did you get for a value?

  23. haterofmath
    • 2 years ago
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    39

  24. hsmt
    • 2 years ago
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    that would be the correct answer. nicely done.

  25. haterofmath
    • 2 years ago
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    ok..thanks...its all starting to make sense now

  26. hsmt
    • 2 years ago
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    good. do you have any other questions? I am not paid by the hour lol

  27. haterofmath
    • 2 years ago
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    lol. no not tonight

  28. hsmt
    • 2 years ago
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    well, then, i hope you have a lovely evening. take care and good nite

  29. haterofmath
    • 2 years ago
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    thanks and the same to you

  30. hsmt
    • 2 years ago
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    :))

  31. haterofmath
    • 2 years ago
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    what happens if the limit is being taken from the left?

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