## GoldRush18 3 years ago Find the limit of:

1. GoldRush18

im posting it

2. GoldRush18

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

3. GoldRush18

x tends to 2

4. GoldRush18

it did not specify it just says find the limit

5. satellite73

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

6. GoldRush18

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

7. GoldRush18

@matt1888 how do i factor the numerator

8. 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.

9. satellite73

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

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

11. GoldRush18

thanks @satellite73 @experimentX and @matt1888 :)

12. experimentX

yw

13. satellite73

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

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

15. 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 :)

16. GoldRush18

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

17. satellite73

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

18. GoldRush18

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

19. GoldRush18

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

20. satellite73

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

@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

@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

Calculus at Pre- University