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GoldRush18

Find the limit of:

  • one year ago
  • one year ago

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  1. GoldRush18
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    im posting it

    • one year ago
  2. GoldRush18
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    \[\lim_{x \rightarrow 2} x^3-8 \div x^2-6x+8\]

    • one year ago
  3. GoldRush18
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    x tends to 2

    • one year ago
  4. GoldRush18
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    it did not specify it just says find the limit

    • one year ago
  5. satellite73
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    if you replace x by 2 and get \(\frac{0}{0}\) then factor and cancel

    • one year ago
  6. GoldRush18
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    @satellite73 i know but thats not the answer i think i would have to factorize the denominator

    • one year ago
  7. GoldRush18
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    @matt1888 how do i factor the numerator

    • one year ago
  8. experimentX
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    \[ \lim_{x \rightarrow 2} \frac{x^3 - 8}{x^2 - 6x + 8} = \lim_{x \rightarrow 2} \frac{(x - 2)(x^2 + 2x + 4)}{(x-2)(x-4)}\] Cancel out \( (x- 2) \) on both numerator and denominator and put the values of x to get your limit.

    • one year ago
  9. satellite73
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    and if you do get \[\frac{0}{0}\] when replacing x by 2 you know how it factors, it must be \[\frac{(x-2)(\text{something})}{(x-2)(\text{something else})}\]

    • one year ago
  10. satellite73
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    don't forget, if you know a zero of a polynomial you know how it factors

    • one year ago
  11. GoldRush18
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    thanks @satellite73 @experimentX and @matt1888 :)

    • one year ago
  12. experimentX
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    yw

    • one year ago
  13. satellite73
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    in other words it is not a miracle that both numerator and denominator have a common factor of \((x-2)\) they must have a common factor

    • one year ago
  14. satellite73
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    also don't forget (because you will see it again) that \[a^3-b^3=(a-b)(a^2+ab+b^2)\]

    • one year ago
  15. GoldRush18
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    yes i do and i have more questions coming up because i'm preparing for Final exams so i really would appreciate the help from you all :)

    • one year ago
  16. GoldRush18
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    @satellite73 whenever i see a equation like that in the numerator i keep forgetting that rule

    • one year ago
  17. satellite73
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    don't forget for the test! also know that \(a^3+b^3=(a+b)(a^2-ab+b^2)\)

    • one year ago
  18. GoldRush18
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    @matt1888 im gonna write them down until i know it and btw how was your test?

    • one year ago
  19. GoldRush18
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    if i could i would have given you all a medal :D

    • one year ago
  20. satellite73
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    not to be picky @matt1888 (and byw congratulation on finishing your final) but you cannot "foil it out" because a) it is three terms by two terms and b) you are factoring, not multiplying, so unless you know the answer you will probably not be able to get it (although you could divide is suppose)

    • one year ago
  21. GoldRush18
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    @matt1888 thats awesome i want to aim high in my finals and go in there with confidence but i have some real issues doing graphs, deferentiation and integration and so forth

    • one year ago
  22. GoldRush18
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    @matt1888 i will let you know when i look back on the topics these are just past paper questions im going through now

    • one year ago
  23. GoldRush18
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    Calculus at Pre- University

    • one year ago
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