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Unformatted text preview: (0, 1) Є R, so there exists a solution. ðf/ðx = 2x is also always continuous on the rectangle R and the point (0, 1) Є R, so the solution must be unique. t x observation2 ~ 10 4 ~ 4 x(2) is outside the window2 ~ 2 0~15 the curve stops when t is near 1 0.92 ~ 0.95 14.3 ~ 15.1 the curve stops when t = 0.933, cannot find x(2) 4. dx/dt = x^2 ∫dx/x^2 = ∫dt1/x = t + c x= 1/(t+c) x(0) = 1/c = 1 c = 1 x = 1/(t1) = 1/(1t)2 2 4 6 8 10 5 10 15 20 25 30 t x x ' = x 2 Figure1 Figure2 2 2 4 6 8 104321 1 2 3 4 t x x ' = x 2...
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 Spring '08
 CHO
 Existence, Continuous function, existence theorem, rectangle R., dx/x=2dt/t lnx, b. tx

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