Question

Find the limit of:

Answer 1

im posting it

Answer 2

\[\lim_{x \rightarrow 2} x^3-8 \div x^2-6x+8\]

Answer 3

x tends to 2

Answer 4

it did not specify it just says find the limit

Answer 5

if you replace x by 2 and get \(\frac{0}{0}\) then factor and cancel

Answer 6

@satellite73 i know but thats not the answer i think i would have to factorize the denominator

Answer 7

@matt1888 how do i factor the numerator

Answer 8

\[ \lim_{x \rightarrow 2} \frac{x^3 - 8}{x^2 - 6x + 8} = \lim_{x \rightarrow 2} \frac{(x - 2)(x^2 + 2x + 4)}{(x-2)(x-4)}\]

Cancel out \( (x- 2) \) on both numerator and denominator and put the values of x to get your limit.

Answer 9

and if you do get
\[\frac{0}{0}\] when replacing x by 2 you know how it factors, it must be
\[\frac{(x-2)(\text{something})}{(x-2)(\text{something else})}\]

Answer 10

don't forget, if you know a zero of a polynomial you know how it factors

Answer 11

thanks @satellite73 @experimentX and @matt1888 :)

Answer 12

yw

Answer 13

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

Answer 14

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

Answer 15

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 :)

Answer 16

@satellite73 whenever i see a equation like that in the numerator i keep forgetting that rule

Answer 17

don't forget for the test! also know that \(a^3+b^3=(a+b)(a^2-ab+b^2)\)

Answer 18

@matt1888 im gonna write them down until i know it and btw how was your test?

Answer 19

if i could i would have given you all a medal :D

Answer 20

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)

Answer 21

@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

Answer 22

@matt1888 i will let you know when i look back on the topics these are just past paper questions im going through now

Answer 23

Calculus at Pre- University