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You are not logged in. #1 20060103 11:05:42
Behavior of a graph at a pointWhich of the following describes the behavior of y = cubicroot(x + 2) at x = 2 #2 20060103 11:15:29
Re: Behavior of a graph at a pointI don't know what is corner, but I think cusp is something like this: IPBLE: Increasing Performance By Lowering Expectations. #4 20060103 11:22:46
Re: Behavior of a graph at a pointPlot: Last edited by krassi_holmz (20060103 11:23:24) IPBLE: Increasing Performance By Lowering Expectations. #5 20060103 11:23:50
Re: Behavior of a graph at a pointNow it's better. IPBLE: Increasing Performance By Lowering Expectations. #6 20060103 11:28:15
Re: Behavior of a graph at a pointFor uploading an image direct to the forum use "post reply" or when you've written your quick post, simply edit it. There you can specify the number of images and the path to be uploaded. IPBLE: Increasing Performance By Lowering Expectations. #7 20060103 11:32:47
Re: Behavior of a graph at a pointok, so my grpah doesn't look like that.. so it doesn't have a cusp, correct? #8 20060103 11:37:56
Re: Behavior of a graph at a pointI just noticed that it isn't differentiable either... #9 20060103 12:35:36
Re: Behavior of a graph at a pointYes, it isn't differenciable. And I don't know what is corner, too. Try at Last edited by krassi_holmz (20060103 12:36:10) IPBLE: Increasing Performance By Lowering Expectations. #10 20060103 14:33:43
Re: Behavior of a graph at a pointf(x) = abs(x), a corner exists at f(0). It is literally a corner. Multiplying this by we get: Now x+2 approaches 0 as x approaches 2. But we know that f(x)^(1/3) > f(x) if f(x) < 1. So the numerator gets (relatively) larger and the denominator gets smaller as x approaches 2. Therefore the slope approaches infinity, and you have a verticle tangent. Last edited by Ricky (20060103 14:36:15) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #11 20060103 20:49:22
Re: Behavior of a graph at a pointD! IPBLE: Increasing Performance By Lowering Expectations. #12 20060104 04:21:43
Re: Behavior of a graph at a pointOy, I completely missed a much more direct way to do the limit: Since x+2 approaches zero as x approaches 2, x+2 is very close to 0 before it gets there, in other words, very small. (x+2)^(1/3) then also becomes increasingly small, and multiplying this by 3 has basically no effect as it will also become increasingly small. So 1 over this means it goes towards infinity. Last edited by Ricky (20060104 04:22:19) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #13 20060104 21:51:57
Re: Behavior of a graph at a pointIt depends of which side you are limiting. If x < 2 and x > 2 then x+2<0 and 1/(x+2) > oo. IPBLE: Increasing Performance By Lowering Expectations. #14 20060105 01:51:21
Re: Behavior of a graph at a pointTrue, but in this case, it doesn't matter. If it approaches negative infinity or infinity from either direction, it is still a vertical tangent. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #15 20060105 02:05:11
Re: Behavior of a graph at a pointYes, yes, just for exactude. IPBLE: Increasing Performance By Lowering Expectations. 