What are the limits of the given functions at x = 0 and x = -1?

[NATURE.M]

Homework Statement

a. lim
x→0

(x^3 − 2x + 7)/(3x^2 − 3)


b. lim
x→-1

1/(x+1)

Homework Equations

The Attempt at a Solution

For a. I obtained a limit of 7/-3
For b. the limit does not exist

(I really unsure about this)

 

[STEMucator]

They both look good. Could you elaborate on part (b) a little more though?

 

[NATURE.M]

They both look good. Could you elaborate on part (b) a little more though?

Thanks.

For b:

lim 1/(x+1) = ∞ (+)
x→-1 (+)

lim 1/(x+1)= ∞ (-)
x→-1 (-)

Therefore, lim 1/(x+1)=undefined
x→-1

 

[Dick]

Thanks.

For b:

lim 1/(x+1) = ∞ (+)
x→-1 (+)

lim 1/(x+1)= ∞ (-)
x→-1 (-)

Therefore, lim 1/(x+1)=undefined
x→-1

That's just fine.