1/x-1/3
divided by
x-3
limit x approaches 3
2007-09-04 14:01:42 · 3 answers · asked by delsolbutterfly 1 in Science & Mathematics ➔ Mathematics
Hint: combine the fractions 1/x - 1/3 into one fraction.
2007-09-04 14:06:33 · answer #1 · answered by Demiurge42 7 · 0⤊ 0⤋
(1/x - 1/3) / (x - 3)
Combine the terms in the top:
1/x = 3/3x and 1/3 = x/3x So:
1/x - 1/3 = 3/3x - x/3x = (3 - x)/3x
Put back into original equation:
[ (3 - x)/3x] / (3 - x)
Now: (3 - x) / (x - 3) = -1 So:
[ (3 - x)/3x] / (3 - x) = -1/3x
At x = 3 the limit becomes -1/3x = -1/9
The effects of approaching from a minus direction and a plus direction should also be thought about just to be on the safe side. When x is a little less than 3 then the expression is of the form (+)/(-) which is negative. When x is a little greater than 3 then it is of the form (-)/(+) and it is also negative.
2007-09-04 21:13:20 · answer #2 · answered by Captain Mephisto 7 · 0⤊ 0⤋
wow i'm re-learning myself. used the hint and got the top as
(3-x)/3x
Factoring and canceling left me with...
-1/3x, so the answer is -1/9?
2007-09-04 21:21:13 · answer #3 · answered by ryuku32 3 · 0⤊ 0⤋