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GoldRush18 Group Title

Find the limit of:

  • 2 years ago
  • 2 years ago

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  1. GoldRush18 Group Title
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    im posting it

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

    • 2 years ago
  3. GoldRush18 Group Title
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    x tends to 2

    • 2 years ago
  4. GoldRush18 Group Title
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    it did not specify it just says find the limit

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

    • 2 years ago
  6. GoldRush18 Group Title
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    @satellite73 i know but thats not the answer i think i would have to factorize the denominator

    • 2 years ago
  7. GoldRush18 Group Title
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    @matt1888 how do i factor the numerator

    • 2 years ago
  8. experimentX Group Title
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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.

    • 2 years ago
  9. satellite73 Group Title
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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 \[\frac{(x-2)(\text{something})}{(x-2)(\text{something else})}\]

    • 2 years ago
  10. satellite73 Group Title
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    don't forget, if you know a zero of a polynomial you know how it factors

    • 2 years ago
  11. GoldRush18 Group Title
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    thanks @satellite73 @experimentX and @matt1888 :)

    • 2 years ago
  12. experimentX Group Title
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    yw

    • 2 years ago
  13. satellite73 Group Title
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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

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

    • 2 years ago
  15. GoldRush18 Group Title
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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 :)

    • 2 years ago
  16. GoldRush18 Group Title
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    @satellite73 whenever i see a equation like that in the numerator i keep forgetting that rule

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

    • 2 years ago
  18. GoldRush18 Group Title
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    @matt1888 im gonna write them down until i know it and btw how was your test?

    • 2 years ago
  19. GoldRush18 Group Title
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    if i could i would have given you all a medal :D

    • 2 years ago
  20. satellite73 Group Title
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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)

    • 2 years ago
  21. GoldRush18 Group Title
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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

    • 2 years ago
  22. GoldRush18 Group Title
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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

    • 2 years ago
  23. GoldRush18 Group Title
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    Calculus at Pre- University

    • 2 years ago
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