O Prove 1+3+ 9+27+ ·+ 3n-1 = 3"-1 for any positive integer n. %3D

Q: 5. Evaluate determinant D by: c. Chios Method 6 4 12 16 6 8 8 14 14 4 A = 4 6 16 12 2 2 10 18 10 14…

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Q: (2) Compute the value r' sin(2r)dr and show the computations involved. If you are using substitu-…

A: (2) Consider the given integral, I=∫0π4x2sin2xdx Use the integration by parts method which is…

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Q: Problems 1-16, evaluate the given integral along the indicated contour. |(2+3) dz, where C is a 2t,…

A: Note: As you highlighted the Question1 so I answered here only Question1.

Q: 24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1)2, 1)-1 1:

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Q: Which of the following statements is (are) false if all vectors are in R"? O None of the statements…

A: Given all vectors in R^n .

Q: dx 1+ax log 1-ах ) Evaluate

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Q: In Problems 31-34, a function and its graph are given. In each problem, find the domain. Vx - 1 x +…

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Q: Problem 3. Recall that a" = for all a > 0 and all b. lim (1+ -)" (1) Compute the limit lim (1+ -)"…

A: 1)  We need to find , limn→∞ 1 + 1nn First we will breakdown 1 + 1nn using binomial theorem ,  1 +…

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Q: 1- Show that the following subset is a subgroup. H = {0 e S, l0(n) = n}c S,

A: We have ,  H = σ ∈ Sn / σn = n  Here , H is subset of Sn Clearly , identity permutation is in  H.…

Q: Evaluate L{t(uo - u1) +tu}.

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Q: (1/2 sin e cos 1 (cos a cosec 8) de (1-cos a ||

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Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}. 1…

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Q: [x 1+t 5. Determine the distance between the point (4, 3, 2) and the plane y 2+s z = 3+5+t a. 3.69…

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Q: Recall that the radius of convergence R of a power series with coefficients a, is found by first…

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Q: Use a triple integral to find the volume of the region bounded by z = 7x + 4y, z = 5, and the planes…

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Q: Find T(t) and N(t) at the given point. r(t) = (t – 4)i + tj; t = 4 T(4) =

A: Given that rt=t2−4i+tj, t=4

Q: Use (1) X = eAtc (1) to find the general solution of the given system. 1 1 1 X' = 1 X 2 -2 -2 | X(t)…

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Q: Exhibit a commutative ring R and an element x E R such that Z CR and x is NOT prime but irreducible…

A: Take R = Z[i√5]  Clearly, R is commutative ring and Z ⊆ R  Also, 2,3 ∈ R are not prime but…

Q: TT tan x sec?x dx 2 O none of them is an impróper integral of type I that diverges is an improper…

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Q: 26.1. Locate and determine the order of zeros of the following functions: (a). e2z - e, (b). z2 sinh…

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Q: Q.6 Choose all the correct options (a) S: dz Over C = -2ni, where C: |z|=4. sin hz (Б) f dz Over C =…

A: To find: Which of the given options are true.   Cauchy residue theorem: If C is a simple, closed,…

Q: Its known that y, = y2(x) = are solutions for the differential equation x²y" – by = 0 the general…

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Q: Using the grometrik pproach we wart to Maximier the objective function 2-72+y subject to the…

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Q: Find the curvature and the radius of curvature at the stated point. T r(t) = 11 cos(t)i+ 10 sin(t)j+…

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Q: Given y1 (t) = t and y2(t) = t- satisfy the corresponding homogeneous equation of t'y" - 2y = - 3t –…

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Q: A school is constructing a rectangular play area against an exterior wall of the school building. It…

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 351 2

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Q: 2) Solve the following initial value problem if t 1 if t 1 y(0) = y'(0) = 0.

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Q: Exercise (3-2): find Fourier series on [0,2n] Question Answer (1) f f(x)%=sinx sin x (4) f(x)=cos x…

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Q: Solve the given ODE using Laplace Transform y"(t) – 6y'(t) – 2y(t) = 4 cos 2t - 4t³; y(0) = –2,y'(0)…

A: First we will take the laplace transform of both sides then we will use the initial condition and…

Q: The integral TT tan x sec?x dx 2 O none of them is an impróper integral of type I that diverges is…

A: Improper integral

Q: Use the level curves in the figure to predict the location of the critical points of f and whether f…

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Q: Exercise 5.3.12. Suppose a E G with |a| = n < ∞ and there is k e Z such that ak multiple of n. = e.…

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Q: .Using &-8 definition show that x3 – 4 lim x→2 x2 + 1 - 4 4 - + in

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Q: Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic…

A: Introduction: The formula for finding the volume of a solid by triple integral is given by,…

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Q: B: The temperature at any point in circular metal plate centered at the origin is, T(x, y) = 100…

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Q: MaxZ = 3X, + X, + 2X; %3D Sto 12X, +3X, +6X, +3X, =9 8X, + X, - 4X; + 2X; = 10 3X; - X, =0 X, 20.j…

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Q: In a population of statistics students it was found that the mean score on the final is 150 with a…

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Q: (1) (2)

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Q: d²y dy + 2b +y = 0 dx dx2

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Q: 5) Find the volume of the solid of the region common to the interiors of the cylinders x2 + = 1 and…

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Q: (a) Consider the following Graph G in a Graph Database: V11 {V10 V9 V12 V: V8 V6 Figure 5: Graph G…

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Q: Problem 22.8 Solve by Laplace transform Uu - 9urr = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u (x,0) = 0,…

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