## GoldRush18 Group Title Find the limit of: 2 years ago 2 years ago

1. GoldRush18 Group Title

im posting it

2. GoldRush18 Group Title

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

3. GoldRush18 Group Title

x tends to 2

4. GoldRush18 Group Title

it did not specify it just says find the limit

5. satellite73 Group Title

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

6. GoldRush18 Group Title

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

7. GoldRush18 Group Title

@matt1888 how do i factor the numerator

8. experimentX Group Title

$\lim_{x \rightarrow 2} \frac{x^3 - 8}{x^2 - 6x + 8} = \lim_{x \rightarrow 2} \frac{(x - 2)(x^2 + 2x + 4)}{(x-2)(x-4)}$ Cancel out $$(x- 2)$$ on both numerator and denominator and put the values of x to get your limit.

9. satellite73 Group Title

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 Group Title

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

11. GoldRush18 Group Title

thanks @satellite73 @experimentX and @matt1888 :)

12. experimentX Group Title

yw

13. satellite73 Group Title

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 Group Title

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

15. GoldRush18 Group Title

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 Group Title

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

17. satellite73 Group Title

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

18. GoldRush18 Group Title

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

19. GoldRush18 Group Title

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

20. satellite73 Group Title

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 Group Title

@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 Group Title

@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 Group Title

Calculus at Pre- University