Calculus: Finding the limit for the given F(x) x^2 -6x / x^2 -x -2?

Question

Alright, quick question to pick at a math heads brain. I was given an assignment and came across a problem im having some trouble with. As it reads, (keep in mind this is for dealing with limits as its approaching -1)

Consider the following F(x): x^2 - 6x / x^2 - x - 2

there are 11 diff x values on the table.

0, -.05, -.9, -.95, -.99 -.999, -2, -1.5, -1.1, -1.01, -1.001

i have to plug in each value for the corresponding X value of the function to receive 11 different answers essentially. When i do so and come out with an answer I'm getting it wrong on my math lab. Can anyone enlighten me on this problem please!

Answer 1

It's not clear to me what problem you're having.

F(0) = 0

F(-.05) = -0.155327342

F(-.9) = -2.14137931

F(-.99) = -231.4414716

F(-.999) = -2331.444148

F(-2) = 4

F(-1.5) = 3.5625

.

.

.F(-1.001) = 2335.221926

The denominator of F(x) is zero at x = -1 (and the numerator is nonzero). These data illustrate that as you approach x = -1 from the left, the value of F is negative and becomes larger and larger in value. If you approach x = -1 from the right, though, the value of F is positive and becomes larger and larger in value. This suggests (but does not prove) that

lim F(x) = -∞

x→-1-

whereas

lim F(x) = ∞

x→-1+

so the (two-sided) limit does not exist.