Solve the following heat equation = ut (x, t) u(0, t) = t, u(1,t) = 0, u(x,0) = x². Uxx (x, t) + x sin(t),

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A: As per the guidelines I am answering only first question.

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Q: n=1 n√n Q5: Find the area shared by the cardioid r = 1 + cos and the circle r = 3 cos 0. Graph the…

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A: Consider the following figure. Here, O is the center. And ∠P=∠Q=90°.

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Q: 29. Evaluate (a) 2π (b) To 5² 2л (c) T Jo (d) the following integrals. 1 + cos 0 -do 2- sin 0 sin² 0…

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Q: f(z) = * The residues of 4z (z − 1)(z + 2)² 4/9.4/9 4/9,-4/9 -4/9, 4/9 4/7,-4/7 -4/9,-4/9

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