limits: (x^3+1)/(x^3+3x^2+3x+1) as x -> -1

[marshmello87]

I don't know how to do these at all.

a) Find the limit of (x^3 + 1) / (x^3 + 3x^2 + 3x +1) when x ---> -1

b) Evaluate when (x^3 - 1) / (x-1)

 

[pka]

What have YOU done on these problems?
Have you tried to factor the expressions.
Note that if x=a makes a polynomial 0 the x-a is a factor.
Show us some work on your part.

 

[marshmello87]

ok for b. i knwo that x-1 is going to be a factor but how am i suppose to expand
x^3 - 1? . i just need steps...and i can do it from there. sorry i didnt mean for it to sound like i just wanted the anser.

 

[galactus]

how am i suppose to expand
x^3 - 1?

Now, Now, you're in calculus :roll: . You're forgetting your basic algebra. How about the difference of 2 cubes?.

 

[marshmello87]

oh ok so (x- 1)( x^2 + 1) / (x-1)

and both (x-1) cancel out?
and im left with x^2 +1? and i substitue x = 1?

 

[tkhunny]

(x- 1)( x^2 + 1)

Multiply those two factors and see if you get x^3 - 1.