i. If n is positive integer, Find (√3+ i)” + (√3 − i)”. ii. Separate tanh-¹(x + iy) into real and imaginary parts.

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Q: Convert the following differential equation into a Perfect equation and then Find its general…

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Q: upper bound for Erland |Es

A: Trapezoidal rule Tn=∆2∑fxn-1+fxnn Simpson's rule Sn=∆x3fxo+4fx1+2fx2+....+4fxn-1+fxn where ∆ is…

Q: Let T R2 R2 be a linear transfor [3] into the vector a (i) T maps vector u

A: Introduction: A linear transformation could be a operation from one vector area to a different one…

Q: PART#A Use Stokes' Theorem to find the circulation of F= (zy, y, z) around the boundary of the…

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Q: Given the functions y = 5x − x2 and y = x. (Sketch the graph) Solve for the surface area of y=x fro…

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Q: Find all three incongruent solutions to the congruence x³ = 1 (mod 103). Express these solutions as…

A: The solutions are obtained by knowing the definition of primitive roots and applying them carefully.…

Q: c. If you had extra-physical powers and could make a spring with a negative spring constant (but…

A: Given: The harmonic oscillator equation, md2ydt2+bdydt+ky=0. The spring has a negative spring…

Q: 5) For each + ive integer i, where i is equal to three, then find the union and intersection of…

A: 5 Given that Ai=x∈R|−1i<x<1i=−1i,1i. a We have to find the A1∪A2∪A3 and A1∩A2∩A3. Here,…

Q: ) Suppose that in a class, there are n many boys and n many girls. Among these 2n many people, we…

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Q: Use power series to evaluate the limit. lim as x goes to 0, (e^x-(1+x))/x^2

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Q: Evaluate L {e-3(1-2) - 1¹e³¹ − 21²cos(2t) + 3e¯'sin(3t+ π) +-π)}

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Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

A: Use the following results, to obtain the solution. The complement of an open set is closed. A set…

Q: Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

A: Solution : The palne 2x+y+2z=8 can be written as                            x4+y8+z4=1 and graph of…

Q: 4. 5. For n E N, { x ER | |x-x*|<1/n } is open. UA_n is open where A_n=(n-1,n).

A: To determine: If the given statements are always true, sometimes true, or never true: (4.) For n∈ℕ,…

Q: 8. Find two linearly independent power series solutiions centered at x = 0 to the differential…

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Q: 1) ²₁²(x² + y²) dxdydz Convert the integral to cylindrical coordinates and integrate.

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Q: The sphere shown below has radius 12 meters. }x X We are trying to find the volume by making…

A: The radius of the sphere is given as 12 meters. The horizontal slices are made in the sphere x…

Q: Special Function Values. Find the values of 45. cosh (1 + i)

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Q: 5. Solve the system by using the matrix exponential 0 1 0 *-[2] + [2]· --[] x' = x x(1) = -3t 3

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Q: Solve the system of equations below both GRAPHICALLY and ANALYT- ICALLY. If the system has no…

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Q: 1. A student listed 10 of his classmates' scores: 34, 42, 27, 34, 45, 32, 31, 44, 33, 31 a.…

A: We know that the median is the value which separates the higher half of the data set, from the lower…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: Determine whether the given linear operator/matrix is diagonalizable. (a) T: R³ → R³ with T(1, 1, 1)…

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Q: In Exercises 41 to 62, perform the modular arithmetic. 1. (9+15) mod 7 3. (5 +22) mod 8 2. (12+8)…

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Q: 6. Prove that for all n E w, the equality 0 n = 0 holds.

A: We will prove by induction. We need to prove for all n∈w, the equality 0·n=0 holds Let n=1, then,…

Q: Prove for all m, n, and k in w, that (m⋅n)k = mk.nk.

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Q: π 1 1+ sin²x 0 dx

A: The given problem is to evaluate the given definite integral of the function 1/(1+sin2(x)) over the…

Q: Basic PDEs Which of the following statements is guaranteed to be true? a O [y + 2x² cos(y)] = 1- 2x²…

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Q: 7. Yoshi is experimenting with an image-editing program on his computer. He rotates his picture…

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Q: Solve AABC. Round decimal answers to the nearest tenth. A 23 14 'В 25 O A B C~° O

A: To find The angles in a triangle.

Q: et f(x) = n 0, if xe Qor x = 0 if x= min lowest term . Compute for ff. " n

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Q: in number 1, B is the matrix representation of Z with respect to B only, not B and B'. The formula…

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Q: Can someone show me how to make the truth table? Can someone show me. Example : All poets are…

A: Introduction: A truth table demonstrates how the truth or falsity of a compound statement is…

Q: 6. [s] Set up only a triple integral that will give the following: (a) the volume of R using…

A: Only draw the solids by hand.

Q: Use Euler's method with step length h = 0.5 and determine an approximate value for y(3) for the…

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Q: Let G = Z9 x Z12 × Z16. (a) Find all subgroups of G of order 144. (b) Let H = ((3,3, 6)), the cyclic…

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Q: Given the following matrices Find the following: 3. BA 4 D + AB A = D = 1 3 1 - 0-4 5 3 3 6 E = 7 2…

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Q: 31-35 Analytic Functions. Find f() = u(x, y) + iv(x, y) with u or u as given. Check for analyticity.…

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Q: Prove by induction Ein (-i)i ;2= (-1)" n(n+1) i=o 2

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Q: (b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n

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Q: I let be a sequence sit. anti =antant 2 for 0191192 iny 2 then b'mom=? n→∞

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Q: Find the Inverse Laplace Transforms of the following. 4 1) | S-3

A: We will use laplace transformation table to find inverse laplace transformation

Q: Use Euler's method with step length h = 0.5 and determine an approximate value for y(3) for the…

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Q: Tom Leonard, of Leonard, Spitz, and Wareham takes an average of 1 hour and 45 minutes to write an…

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Q: b) Let T:R³ R¹ be a linear transformation, and let B = {e1, ez, e3} be the standard basis for R³.…

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Q: Suppose Ch is a segn of real numbers such that lim /cn/h exists and is non-zero. If the ROC the…

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Q: 2. Evaluate dx a. ·S= x√x-1

A: As per the policy we are allowed to answer only one question at a time. So, I am answering the first…

Q: Q4) (a) Use separation of variables method to solve the partial differential equation: d'u du + = U…

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Q: I. 1 Evaluate each determinant. 3 -3

A: The given determinant is -431-3 ={(-4)×(-3)}-(3×1) =12-3 =9