Question

Find the limit (if it exists).

lim (6x^2 + x − 1) /(6x^2 − 3x − 3)
x→(−1/2)+

Answer 1

i've tried both + and - infinity, and I know there's an asymptote around 1, but I can't figure it out...

Answer 2

when I see this , first thing I instinctively do is factor

3(x-1)(2x+1)

Answer 3

^ that was denominator

Answer 4

do you then set the factors equal to zero to find the limits?

Answer 5

x=1 and -1/2?

Answer 6

numerator

(2x+1)(3x-1)
----------------
3(2x+1)(x-1)

now cancel out

(3x-1)
-----------
3(x-1)

now evaluate

Answer 7

how do you evaluate it? by subbing in -1/2?

(3*-0.5)-1 / (3(-1.5)

=-2.5 / -4.5

Answer 8

=5/9

Answer 9

yes

Answer 10

really? Yess!!

Answer 11

thank you thank you!!

Answer 12

i understand!

Answer 13

I think you did