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**HA7 / Re: HA7-P4**

« **on:**November 05, 2015, 04:49:45 PM »

I think I am also wrong for part d. But general formula is right, just do derivative to get final answer.

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I think I am also wrong for part d. But general formula is right, just do derivative to get final answer.

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Thanks. Hope I get correct answer this time

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This is my answer for part b. I am not sure whether I do calculation correctly.

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Solution of part b is attached. Please correct me if I am wrong.

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Solution for a(i) is attached. Please correct me if I am wrong.

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This is my answer for question1(a), the prove part.

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Where does 1\3 Ï•(0) come from ?

When I plug numbers into graph which was posted by prof, I do not get this term.

When I plug numbers into graph which was posted by prof, I do not get this term.

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For (d). The following is my answer.

Given u is continuous when r=0, which means lim_{râ†’0} u(r,t) exists.

Then lim_{râ†’0} [f(r+ct) + g(r-ct)] = 0. Because otherwise, lim_{râ†’0} [f(r+ct) + g(r-ct)] â‰ 0 implies lim_{râ†’0} u(r,t) tends to be infinity.

So f(ct) + g(-ct) = 0

f(ct) = - g(-ct)

-f(x) = g(-x)

So g(r-ct) = -f(ct-r). As a result, u = r^{-1} [f(r+ct) - f(ct-r)]

Given u is continuous when r=0, which means lim

Then lim

So f(ct) + g(-ct) = 0

f(ct) = - g(-ct)

-f(x) = g(-x)

So g(r-ct) = -f(ct-r). As a result, u = r

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For (b), I am thinking (c_{1} + c_{2})^{2} - 4c_{1}c_{2} = (c_{1} - c_{2})^{2} which is always larger or equal to zero. And plug in expression(11), it equals to (c_{1} - c_{2})^{2}.

Given A^{2} always larger than 0 (ignore case of equal 0) so B^{2}- 4AC always larger or equal to 0. We dont need to emphasize on this condition.

Therefore, is it possible the answer is A â‰ 0 ?? I am not sure of this.

Given A

Therefore, is it possible the answer is A â‰ 0 ?? I am not sure of this.

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For (5) I think you miss the last case : x<-ct and xâ‰¥ct

In these conditions, I get (-x+ct)\2c

In these conditions, I get (-x+ct)\2c

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