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GoldRush18

  • 2 years ago

Find the limit of:

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  1. GoldRush18
    • 2 years ago
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    im posting it

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

  3. GoldRush18
    • 2 years ago
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    x tends to 2

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

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

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

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

  8. experimentX
    • 2 years ago
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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.

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

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

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

  12. experimentX
    • 2 years ago
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    yw

  13. satellite73
    • 2 years ago
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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

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

  15. GoldRush18
    • 2 years ago
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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 :)

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

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

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

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

  20. satellite73
    • 2 years ago
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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)

  21. GoldRush18
    • 2 years ago
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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

  22. GoldRush18
    • 2 years ago
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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

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

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