How do you solve this limit?

Question

problem: limit of (2x)/(x-2) as x approaches 2 from the left.

how do you solve this problem without using a calculator?

Answer 1

It's probably not 2.

Use values of x really close to 2, but smaller since you want the left hand limit.

if x=1.9 2x/(x-2)=-38

if x=1.99 2x/(x-2)=-398

Since there is an asymptote and x=2, we know it either approaches infinity, or negative infinity. Since our values are negative it's fairly obvious which one it is.

Answer 2

You can think of the limit from the left as not quite hitting the number two on the number line.  Substitute 1.9 for x.

[2(1.9)]/(1.9 - 2)

3.8/ -.1 = -38

Answer 3

i beleive the limit would be 2 because if you sub in the 2 for the X, you will have 0 on the denominator, which you cannot have, therefore, the graph does not exist at x=2 =] (i hope i'm right, if not sorry, i haven't done any math work in 4 months, i had calculus and i passed with a B+ so i hope i'm right)