Question

find the limit as x approaches 2 from the left of x/x-2

Answer 1

it's negative infinity, if I'm not mistaken

Answer 2

i know the answer is negative infinity but why? Do i have to plug 2 into the x/x-2?

Answer 3

ok this is why..

Answer 4

it was a homework problem and she gives us the anwers but i dont get how to get negaitve infinity

Answer 5

as x approaches 2 from the left, or:
x=1.99999,
x=1.99999999999,
x=1.99999999999999999,
x=1.99999999999999....999999,
the bottom of that fraction approaches "negative zero"

Answer 6

or the denominator will get very close to:
-0.0000000001,
-0.0000000000001,
-0.000000..........00000001

Answer 7

So as the bottom gets small, the fraction blows up.... but since the bottom is negative and the top is positive, the whole thing approaches negative infinity.

Answer 8

ohh that makes sense now

Answer 9

So do you like my monkey?

Answer 10

so its negative infinity because its approaching 2 from the left?

Answer 11

yea, if it were approaching from the right, it would have been positive infinity.

Answer 12

gotcha. thanks!

Answer 13

because you'd be getting:
2.0000000000000001
2.00000000000000000000000001
so the bottom wld be:
0.0000000001
0.0000000000000000000001
so the whole thing wld approach positive infinity.

Answer 14

By the way, actual limit of x/(x-2) as x approaches 2 doesn't exist. For it to exist the right and left hand limits must equal each other, but here one is negative and one is positive infinity, so the limit does not exist. If both were approaching -inf, the answer wld be -inf, if both were approaching positive inf, the answer wld be positive inf.