h) The solution of the heat flow problem Ut = 3uxx, uz (0, t) = 0, obeys lim u(x, t) = t→∞ uz (1, t) = 0, u(x,0) = x³, t> 0, 0 0, t> 0, 0≤x≤1.

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Q: 2. f(x, y) = (x² + y²)² — 2(x² - y²) + 1. Ans.: global minimum 0 at (±1,0), saddle at (0, 0).

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Q: f(x,y)=x² +16xy + y² +8

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Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule.

Q: 2. Suppose that {f(t)} = F(s) with F a differentiable function and that {f(t)} exists. Then L{-te*…

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Q: f(x, y) = xy(3-a-y) OA. (1, В. О в. (0, 1) O C. (0,0) O P. (-3,3)

A: Given function is f(x,y)=xy(3-x-y) At first we differentiate it partially w.r.t. x and y and setting…

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Q: 17. y = e"(p + p\p)

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Q: F(x,y)= 4xy-x^3-2y^2 C. Find the relative minimum and maximum values of F SHOW ALL WORK!!! thank…

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Q: Demonstrate the use of the method with reflections on the use of numerical methods, find the minimum…

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Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: the

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Q: h(x, y) = xy2/3 + xy x⁹ +2y³ 1 √3' us at the point (0, 0) or not. If not, determ

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Q: Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations: C(t) +…

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