limitsss huhuhuh?

Question

lim y^3 + 8 / y+2
y-> -2


the answer should not be 0/0..

Answer 1

Hi,

y³ + 8
---------
y + 2

is the same as

(y + 2)(y² - 2y + 4)
---------------------------
(y+2)

If you consider the y + 2 factor as cancelled out, then you are really finding

lim....y² - 2y + 4
y->-2

Since y² - 2y + 4 is (-2)² -2(-2) + 4, this equals 4 + 4+ 4 = 12

so........... y³ + 8
.....lim......--------- = 12
.....y->-2...y + 2

I hope that helps!! :-)

Answer 2

This is really asking: What value does this expression approach as y approaches -2.
One method is to plug the -2 in for the y.
You are correct that you then get 0/0 which is called an indeterminate form. Essentially, plugging in gets you no where in this case.
Second option is to do long division. What is (y^3+8) divided by (y+2)?
When you do this division you get:
(y^3+8)/(y+2)=y^2-2y+4)
So the original expression is equivalent to y^2-2y+4.
You can now evaluate that at y=-2.
As y get close to -2 the new expression gets close to 12.
So the limit of the expression as y approaches -2 is 12.
Also, if you graph the first expression and then the equivalent expression you will see they are the same graph confirming that we did the division properly.
You can also now calculate the value of the expression at y = -2.
You should be good to go.

Answer 3

Just see my anser to this same question at

http://answers.yahoo.com/question/index;_ylt=Amgz4usdSao7UOmsWLHwekjsy6IX?qid=20070628063158AA8GUEF&show=7#profile-info-03b8c2352e6f7f56336f74151bbf6800aa