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GoldRush18
 3 years ago
Find the limit of:
GoldRush18
 3 years ago
Find the limit of:

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GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 2} x^38 \div x^26x+8\]

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0it did not specify it just says find the limit

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1if you replace x by 2 and get \(\frac{0}{0}\) then factor and cancel

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0@satellite73 i know but thats not the answer i think i would have to factorize the denominator

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0@matt1888 how do i factor the numerator

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2\[ \lim_{x \rightarrow 2} \frac{x^3  8}{x^2  6x + 8} = \lim_{x \rightarrow 2} \frac{(x  2)(x^2 + 2x + 4)}{(x2)(x4)}\] Cancel out \( (x 2) \) on both numerator and denominator and put the values of x to get your limit.

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1and if you do get \[\frac{0}{0}\] when replacing x by 2 you know how it factors, it must be \[\frac{(x2)(\text{something})}{(x2)(\text{something else})}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1don't forget, if you know a zero of a polynomial you know how it factors

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0thanks @satellite73 @experimentX and @matt1888 :)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1in other words it is not a miracle that both numerator and denominator have a common factor of \((x2)\) they must have a common factor

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1also don't forget (because you will see it again) that \[a^3b^3=(ab)(a^2+ab+b^2)\]

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0yes 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
 3 years ago
Best ResponseYou've already chosen the best response.0@satellite73 whenever i see a equation like that in the numerator i keep forgetting that rule

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1don't forget for the test! also know that \(a^3+b^3=(a+b)(a^2ab+b^2)\)

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0@matt1888 im gonna write them down until i know it and btw how was your test?

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0if i could i would have given you all a medal :D

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1not 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
 3 years ago
Best ResponseYou've already chosen the best response.0@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
 3 years ago
Best ResponseYou've already chosen the best response.0@matt1888 i will let you know when i look back on the topics these are just past paper questions im going through now

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0Calculus at Pre University
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