.. Evaluate. a) 2³ x 4² x 2-3 b) 81¹/4 - 81/3

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Q: n* +2n²+1 no +3 3. Test the convergence of the series an= Ex=1" O Converge O Diverge

A: Given series is an = ∑n=1∞n4+2n2+1n6+3

Q: (a) Assume that f(x, y, z) and F (x, y, z) are arbitrary differentiable functions such that f(x, y,…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 12 Identify the simple graph. (a) (b) (c) V2 "O €2 VI (a) vo (b) VI (c) V2 V3

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Q: .a. Is the set of vectors W = {(x,y,z) x,y,z € R,x=z+2} subspace of R³?

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A: Find the intersecting line L. For any random point on the line L, we can find the general distance.…

Q: Solve a system using the Kramer method 2x + 3y -z = 5 4x + 4y - 3z = 3 -2x+3y-z = 1

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Q: (b)Prove the inequality x² + x² + ... + x² n AI 2 xn ( ³²₁ +2²₂ + ... + x n ) ² n

A: Sol

Q: (b) Find the interval of convergence of the following series Σ (¹+-½)²³ ( (x - 1)" n=1

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Q: (b) Let D be a circular domain of radius R with center at the origin. Show that sin(r² + y²) dr dy…

A: We will first transform the coordinates from Cartesian to polar using x= rcos\theta, y= rsin\theta.

Q: simplification is to isolate terms and identify the dominant term. For instance, we might want to…

A: fx(n) =log2log2n+3for n→∞log2n+3 =log2n

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A: We have given a vector ,  v = 9cos9θ i+ 9sin9θ j We need to find magnitude of vector v. Magnitude of…

Q: Q2A)Matrix 4 = [],find Eigen values of 1² A dy B)Solve differential equation=-(x²+y) dx x+siny

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Q: B)Prove (cose + i sine)" = cosno + i sin no

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Q: (i) Using Picard's approximation method find two iterates of the initial value problem: dy=y+y²,…

A: For a differential equation dydx=fx.y with initial value xo,y0 Picard approximation can be given by…

Q: Calculus A 15m high closed cylindrical vessel. having a volume of 400 m3 is fully filled by oil -…

A: Let us solve the given problem on cylinder in the next steps.

Q: Q1A) The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.

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Q: Proceed as in this example to find the solution of the given initial-value problem. Evaluate the…

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Q: QUESTION 5 A solid G bounded by parabolic cylinders y = x², x = y² and planes z = 1, z = 5. (i)…

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Q: (sin³r} = {1-co52} and find the Laplace transform: S 1 2 -3²+2 S 1 2 O 1(1 1/1 S +4 +2

A: Given formula of sin^2 t is in terms of cos2t. For detailed solution, visit step 2.

Q: Graph the feasible region for the follow system of inequalities by drawing a polygon around the…

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Q: Use the Karush-Kuhn-Tucker method for the below optimisation problem and discuss any conclusions…

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Q: Invert the Z-transform. X(z) z(2²-22-1) (2²-4z + 3)(z-2)

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Q: B)Convert r = √2 cos(0-7) = √2 cos(0-) to cartesian.

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Q: Advanced Math Question

A: Use the result  The inscribed angle( measure of angle on the circumference) is half the measure of…

Q: Use the quotient law for tensors to show that the array -2xy -2xz /y²+z²-x² -2yx x²+z²-y² -2yz -2zx…

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Q: Spencer manages a store that sells speakers. Each Master Blaster takes 36 hours to create the…

A: We have to find the number of each of the speakers to make the most revenue.

Q: 4x + y dy x + 2y dt a) Find the general solution for x(t) and y(t) b) Solve the initial value…

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Q: B)Is w = Zez analytical function or not?

A: Here we use the Cauchy Riemann equations to show that the function is analytic or not. At follows

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Q: fy=sin-¹ find Zy

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Q: Suppose that f: R2 → R is a function given by y³ x² + y² f(x, y) {+ for x = y = 0. Show that f(x, y)…

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Q: 5. Solve the following simultaneous differential equations: dx dy (i) + 5x + y = et, x + 3y = e²t,…

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Q: The Taylor series of the function f(x) = cosx at x=0 is (1) ²n (-1)"x²n 2n=0 (2n)! En-0 n=0 (2n)! Σ…

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Q: 31 [D-1 D+91 9 B +10)}={} LD-2 2D + 91 1 D-21 13 {} B = 2 = ²16 ²410)} = (7) 10 [2D + 1 D + 3 D + 21…

A: According to our guideline, we can solve only first question of multiple questions. So,here we solve…

Q: whats 065 when $ is oilers Fundion

A: Solving first question.

Q: 3. Test the convergence of the series an O Converge O Diverge O Fail test 100 2n=1 n*+2n²+1 75 +3

A: We will check whether the given series convergence or divergeent .

Q: If L {f(t)} = F(s) then L{t"f(t)} = (−1)n dm F(s) -F'(s) dsn (-1) F(s) (1) F(s) dn dsn dxn خيار 2…

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Q: Solve the initial value problem y" - 5y' - 14y = 0, y(0) = a, y'(0) = 6. Find a so that the solution…

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Q: 15. Find a basis for the row space and the column space of the matrix 132-5 -2 3 671 rank of each…

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Q: Find the solution of the initial value problem y" - 2y3y 15te²t, y(0) = 2, y'(0) = 0. = NOTE: Enter…

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Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: Given curves are y=0 and y = x-x2

Q: SOLVE FOR THE X OF THE FOLLOWING FUNCTION USING BISECTION METHOD b. x³7x² + 14x6 = 0

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Q: Find the general solutions of the system. - 14 -9 0 x' = 1-8 0x 1 x(t) =

A: Please see the attachment

Q: (7) Solve the PDE by Laplace Transform a²w aw <=100 +100 + 25w, ar² at w(x, 0) = 0 if x ≥ 0, we(x,…

A: The given P.D.E is                       ∂2w∂x2=100∂2w∂t2+100∂w∂t+25w,wx, 0=0 if x≥0, wtx, 0=0 if…

Q: what is the directional multiplication of therectors [3₁-1₁2] [ 4.2.1]

A: Follow the steps.

Q: Prove the following assertions using a direct proof. d. If x is odd integer, and y is even integer,…

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