Use a triple integral over spherical coordinates to evaluate (2² + y²) dV, where E is the sphere a² + y² + z² = 1. 2 COS x - 3 sin? x cos x +C Hint: sin x dx 3

Q: 1. Find an equation of the tangent line to the graph of y = In (x² – 3) + e²-* at the point (2, 1).

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A: The detailed solution is given in the attached Handwritten notes.

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Q: 2) 100 The series Cnn) is convagest by direct companso हे 100-1L test with E since it converges forr...

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Q: 1. Let f be continuous on I = [a, b] and let H : I → R be defined by H(x) = | f(t)dt, x € I. Find H'...

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Q: Use the Laplace formulas to get L{f(t)}. 6) f(t) = 1) f(t) = 2t* 7) f(t) =- 2) f(t) = 4t – 10 8) f(t...

A: Since  you have posted a multi subparts question according to guildlines I will solve first  three q...

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Q: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

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Q: solve the following Equations using 4th order Runge- Kutta Method • Equatioras a. y = 2x3 b. y = cos...

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Q: Find the chromatic polynomials of the following graphs (a) (b) (c)

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Q: Evaluate 36 +x² +y dA, T where D = {(x, y) : x > 0, y 2 0, x2 +y < 64}. O 61 49 1036 244 O 392

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Q: п(п+1)(2n+1) Use mathematical induction to prove that 12 +2² +...+n? for any = positive integer n.

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Q: Find the Laplace Transform f (x) = ea. Answer: a. sta 1 C. sta d.

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Q: find the approyimate Valueof: +.

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Q: Evaluate using relaxation method. Tolerance is < 0.0001 Evaluate for the unknown variables -1 = X, +...

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Q: y), the harmonic conjugate of u. Form the

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Q: Suppose the density of a two dimensional figure (see the shaded area below, a sector of a e grams 5L...

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