Can anyone explain to me how to solve the following limit problem? Lim x--3, u^4-81/u^3-27. Any help would be appreciated!

Question

Can anyone explain to me how to solve the following limit problem? Lim x-->3, u^4-81/u^3-27. Any help would be appreciated!

zarkon · Answer

factor the numerator and the denominator

myininaya · Answer

you could also apply l'hospital here

anonymous · Answer

yes, I need to factor and substitution clearly wont work. Having trouble factoring.Hence the request for help :)

myininaya · Answer

do you know how to factor the difference of squares?

myininaya · Answer

$$a^4-b^4=(a^2)^2-(b^2)^2=(a^2-b^2)(a^2+b^2)=(a-b)(a+b)(a^2+b^2)$$

myininaya · Answer

$$a^3-b^3=(a-b)(a^2+ab+b^2)$$

myininaya · Answer

that should be helpful

anonymous · Answer

thank you I was doing  (u^2 +9)(u^2-9). let me take another crack at it and see if I cant factor the denominator. Thanks

myininaya · Answer

yes and u^2-9 can be factor further

myininaya · Answer

factored*

anonymous · Answer

got it, thank you. I realy need t brush up and becme more proficient in basic college algebra skills like square rts and exponents. they still trip me up. The answer is 4 btw :)