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