01-13-2006, 07:41 AM | #1 (permalink) |
Crazy
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linearizing equations
Hey,
Y = [ax + b/x]^1/2 Now, I made this: Y = ax^1/2 + (b^1/2 / x^1/2) Now, I would plot Y vs. X^1/2 for a linear plot, with a slope of a. But whats my intercept ? Or can someone else suggest another way to linearize, or what the intercept is for the plot I just stated. Thanks! |
01-13-2006, 09:30 PM | #5 (permalink) |
Insane
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No, both terms include X so there can be no intercept other than the origin for a truly linear equation, however this isn't linear.
normally you have y = mx + c, which gives the intercept as c, in this case we have two X terms, when we evaluate this as X -> 0 then we get 0a + b/+-0 (a very small number), as such at the origin the actual value is undefined, similar to a tan curve at various points. For large values of X aX dominates the equation and we have a function which says Y^2 = aX or Y = (aX)^1/2, and again for negative X, at the origin the b/X dominates and we have the graph rapidly shooting off to +ve/-ve infinity for +0/-0. |
01-14-2006, 04:39 AM | #6 (permalink) |
Junkie
Location: In the land of ice and snow.
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When i first read this i thought the op was referring to the linearization where you find the equation for the tangent line at any given point on the graph:
L(x) = f(x1)+f'(x)*(x-x1) But now i don't really have any clue what the op needs. |
01-15-2006, 10:52 AM | #8 (permalink) |
Crazy
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Hey,
What I need to do with the original equation, is somehow manipulate it so that it is linear, and I need to specify the slope and y-intercept. So, So, I can plot Y^2 vs. X, where the slope is a, and the intercept is b/x.. That plot does in fact yield a linear line....and the intercept does work out to be b/x. Unless I've messed something up...? |
01-16-2006, 07:08 AM | #9 (permalink) |
Insane
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Well b/x is +/- infinity as x tends to 0... that equation is in no way straight.
Input (8x+8/x)^.5 in this url: http://www.coolmath.com/graphit/ That will show you what the function should look like |
01-17-2006, 08:34 AM | #12 (permalink) |
Insane
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http://www.cbu.edu/~rprice/lectures/lineariz.html
Talks about Taylor expansions and suchlike to approximate a non-linear equation with a linear one. |
01-18-2006, 08:18 AM | #15 (permalink) |
Insane
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Are you trying to fit data to a model to solve for a and b?
If so, you could do this: y^2=ax+b/x xy^2=ax^2+b Plot xy^2 vs. x^2. You'll get an intercept of b, and a slope of a. OR.... y^2/x=a+b/x^2 Plot y^2/x vs 1/x^2. You'll get a intercept of a and a slope of b. |
Tags |
equations, linearizing |
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