GoldRush18
  • GoldRush18
Find the limit of:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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GoldRush18
  • GoldRush18
im posting it
GoldRush18
  • GoldRush18
\[\lim_{x \rightarrow 2} x^3-8 \div x^2-6x+8\]
GoldRush18
  • GoldRush18
x tends to 2

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GoldRush18
  • GoldRush18
it did not specify it just says find the limit
anonymous
  • anonymous
if you replace x by 2 and get \(\frac{0}{0}\) then factor and cancel
GoldRush18
  • GoldRush18
@satellite73 i know but thats not the answer i think i would have to factorize the denominator
GoldRush18
  • GoldRush18
@matt1888 how do i factor the numerator
experimentX
  • experimentX
\[ \lim_{x \rightarrow 2} \frac{x^3 - 8}{x^2 - 6x + 8} = \lim_{x \rightarrow 2} \frac{(x - 2)(x^2 + 2x + 4)}{(x-2)(x-4)}\] Cancel out \( (x- 2) \) on both numerator and denominator and put the values of x to get your limit.
anonymous
  • anonymous
and if you do get \[\frac{0}{0}\] when replacing x by 2 you know how it factors, it must be \[\frac{(x-2)(\text{something})}{(x-2)(\text{something else})}\]
anonymous
  • anonymous
don't forget, if you know a zero of a polynomial you know how it factors
GoldRush18
  • GoldRush18
thanks @satellite73 @experimentX and @matt1888 :)
experimentX
  • experimentX
yw
anonymous
  • anonymous
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
anonymous
  • anonymous
also don't forget (because you will see it again) that \[a^3-b^3=(a-b)(a^2+ab+b^2)\]
GoldRush18
  • GoldRush18
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 :)
GoldRush18
  • GoldRush18
@satellite73 whenever i see a equation like that in the numerator i keep forgetting that rule
anonymous
  • anonymous
don't forget for the test! also know that \(a^3+b^3=(a+b)(a^2-ab+b^2)\)
GoldRush18
  • GoldRush18
@matt1888 im gonna write them down until i know it and btw how was your test?
GoldRush18
  • GoldRush18
if i could i would have given you all a medal :D
anonymous
  • anonymous
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)
GoldRush18
  • GoldRush18
@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
GoldRush18
  • GoldRush18
@matt1888 i will let you know when i look back on the topics these are just past paper questions im going through now
GoldRush18
  • GoldRush18
Calculus at Pre- University

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