Solve the following IBVP: Ut = Urr, 0 0, u(0, t) = 1, u(1, t) = t, t > 0, u(x, 0) = 1 + sin(x) - x, for x = [0, 1). E

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Q: Let u = PQ and v = PR. (a) Write u and v in component form. (4₁, 4₂) = u V P = (-2,-1), Q = (5, -1),…

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Q: b) [-- Determine whether the series Σπορ" n=1 is convergent or divergent.

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Q: USE SPHERICAL COORDINATES TO EVALUATE 2π -2 R²² R² S 2-r r+z (r² + z²)3/2¹ dz dr de

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A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

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Q: 3 LL -3√√√9-x² Jo √9-x²-y² (x² + y² + z²) dz dy dx

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Q: a. b. Find the function g(t) whose Laplace transform is given by graph: T G(T) = (7² + 4)²² Hint:…

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Q: thank you! could you show me how to do d

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Q: Question 1 ] a. [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) =…

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Q: Problem three : Let A and B be the sets of even an odd permutations of Sn respectively. Define 6: A…

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A: Some of the Properties of Laplace transformation  Lsint=as2+a2Lu5(t)=e-5ssLf(t)*g(t)=Lf(t)·Lg(t)

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Q: 3) 4) 1 x-y + 2z - w = -1 2x + y2z2w = -2 -x + 2y4z + w = 1 3x3w=-3 1₁ 21₁-12 + 313 + 4/4 = 9 213 +…

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Q: Evaluate: f(1) Given: F(s)= 1/(s³ + 2s)

A: Given :  F(s) = 1s3+2s To find : f(1)

Q: Suppose the cost c of producing 94 units of product A and q units of product B is given by: c = (3q²…

A: Given that cost c=3qA2+qB2+413 And qA=10−pA+pB2, qB=20+pA−11pB. Also given pA=25 and pB=4. We have…