(a) Solve the initial value problem in explicit form: t ∂u ∂t + (t + u) ∂u ∂x = x − t, u(x, 1) = 1 + x, |x| ≤ 2, sketch typical base characteristics in the xt-plane. Show the subset of R2 in which the solution u(x, t) is defined.

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Q: Exercise 4. Show that the function f is not differentiable at (0,0) f(x, y) = x³ + y³

A: We have given that ,  fx , y = x3 + y33 Here , ∂f∂x = 3x23x3 + y323 ∂f∂x = x2x3 + y323 At , x , y =…

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Q: (b) In(2x2 + у — 23) %3D х

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Q: Q2: Find the absolute maximum and minimum of the function f(x, y) = x² + y² on the closed triangular…

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Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

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Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyx, g(x, y, z) = x²yz, U = x²yi –…

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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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