2007-03-11 17:09:13 · 8 answers · asked by SANCHO 3 in Science & Mathematics ➔ Mathematics
The equation reduces to 3/(x-4). As x approaches 4, the equation becomes of the form a/0:
The left hand side limit is -infinity.
The right hand side limit is +infinity.
As LHL is not equal to RHL, Limit does not exist for this functon at x=4.
Hope this helps. You may mail me if you have any problems with this solution.
2007-03-11 17:16:07 · answer #1 · answered by Shrey G 3 · 1⤊ 0⤋
As others have pointed out the limit is undefined as x approaches 4.
However I think the problem was supposed to be what the limit os as x approaches 1 - even though the numerator and denominator equal 0 when x=1, the limit is defined.
To find it we notice that both numerator and denominator are products of x-1. Dividing both by x-1, we get 3/(x-4) which is -1 for x = 1.
So if what youreally wanted to know is what the limit was as x->1, the answer is -1.
2007-03-12 00:20:36 · answer #2 · answered by vinniepescado 2 · 0⤊ 0⤋
Find the limit of (3x - 3)/(x² - 5x + 4) as xâ4.
Limit as xâ4 of 3(x - 1)/[(x - 1)(x - 4)]
= Limit as xâ4 of 3/(x - 4) = 3/0
The limit diverges.
2007-03-12 00:17:22 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
lim [ (3x - 3) / (x^2 - 5x + 4) ]
x -> 4
I'm going to assume you don't know L'Hospital's rule at this point, so to solve it without resorting to that method, factor top and bottom.
lim [ 3(x - 1) / [(x - 4)(x - 1)] ]
x -> 4
Note the cancellation.
lim [ 3/(x - 4)]
x -> 4
And now, this is of the form [3/0], so the limit doesn't exist.
2007-03-12 00:15:56 · answer #4 · answered by Puggy 7 · 0⤊ 0⤋
This limit does not exist since as x -> 4 from the left, the fraction heads towards negative infinity, but as x -> 4 from
the right, the fraction heads towards positive infinity.
Therefore, the limit does not exist.
2007-03-12 00:14:10 · answer #5 · answered by s_h_mc 4 · 1⤊ 0⤋
Numerator factors to 3(x-1) and denominator factors to (x-4)(x-1). hence if you simplify xnot equal 1, then the new rational is 3/(x-4) which doe not exist.
ANSWER: Does not exist ( +infinity on one side and -infinity on the other)
2007-03-12 00:16:42 · answer #6 · answered by MathMark 3 · 0⤊ 0⤋
(3x-3)/(x^2-5x+4)=3*(x-1)/((x-4)(x-1)
therefore lim as x approaches four of 3/(x-4)...
is infinity (constant/(something really small)=infinity)
2007-03-12 00:16:35 · answer #7 · answered by tobysamples 1 · 0⤊ 0⤋
Infinite. The numerator is finite [9] as the denominator goes to 0.
2007-03-12 00:14:32 · answer #8 · answered by Anonymous · 0⤊ 0⤋