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## GoldRush18 Find the limit of: one year ago one year ago

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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. matt1888

no sorry wrong window @GoldRush18

6. satellite73

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

7. matt1888

factor both numerator and denominator

8. GoldRush18

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

9. GoldRush18

@matt1888 how do i factor the numerator

10. 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.

11. satellite73

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

12. matt1888

@experimentX has you covered on this one

13. satellite73

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

14. GoldRush18

thanks @satellite73 @experimentX and @matt1888 :)

15. experimentX

yw

16. 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

17. matt1888

no problem do you understand how to go about solving these type of problems now?

18. satellite73

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

19. 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 :)

20. matt1888

no problem just took my Calc I final today

21. GoldRush18

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

22. satellite73

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

23. matt1888

or just FOIL it out but that takes a long time so @satellite73 is right that the rules are good to memorize

24. GoldRush18

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

25. GoldRush18

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

26. 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)

27. matt1888

was okay @GoldRush18 probably a high B

28. matt1888

@satellite73 your completely right my apologies my brain isn't working the best right now, time for a nap.

29. 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

30. matt1888

@GoldRush18 graphing what exactly? Using the first and second derivative test?

31. GoldRush18

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

32. matt1888

@GoldRush18 Calc I University or High School?

33. GoldRush18

Calculus at Pre- University

34. matt1888

okay