Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7,-5)

Q: . Prove that the series is divergent. Σ(-1)" n=1

A: We need to prove that , ∑n=1∞ -1n  is divergent. We know that , a sequence of partial sums of series…

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Q: Problem 5 Let A = {m+n√2: m, n e Z). Prove A is countable.

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Q: 1. Iff: [0, 1] → R is defined as f(x)=x if x is rational, 1-x if x is irrational, discuss the…

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Q: Problem 5 Let A = {m+n√2: m, n e Z}. Prove A is countable.

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Q: lim (x,y)→(0,0) x²y (x² + y)²

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…

Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. cos 3t 4.…

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Q: A frequency table of grades has five classes (A, B, C, D, F) with frequencies of 5, 13, 13, 6, and 2…

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Q: Gauss sediel method and jacobi method is the same?

A: We have to see how gauss Jacobi is different with gauss sediel method .

Q: Let be a function that allows continuous second partial derivatives, we know that: Vf(x, y) = (16x³…

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Q: e sequence 1, 1, 3, 7, 17, 41, 99,... is a second-order linear recurrence given by x = 2x₁ + x2 for…

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Q: 3t

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Q: A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on this…

A: We answer only one question at a time , so we will answer the first question since the exact one…

Q: QUESTION 2 Let T(x): R³ R4 be defined by T(e₁)= -3 (a) Compute -4) 5 1 2 [] 2 T(e₂)= 10 and T(e 3)=…

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Q: Use the Laplace transform to solve the given system of differential e dx 4x + d³y dt3 = 12 sin(t) dt…

A: dxdt−4x+d3ydt3=12sintdxdt+2x−2d3ydt3=0x0=0, y0=0, y'0=0, y''0=0

Q: 21 (s+ √2) L-¹ {-

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Q: We are going to fence in a rectangular field. If we look at the field from above the cost of the…

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: 5. You are given the weighted voting system (q: 10,5, 3, 2). (a) What is the highest possible value…

A: Given the weighted voting system  q:10,5,3,2 (a) To find the highest possible value of the quota q…

Q: COMPLEX ANALYSIS Please answer all questions Calculate lim using properties of limits. 5iz-3 2z+6i1…

A: We have to calculate limz→∞5iz-32z+6i

Q: Find the laplace transform of ?(?) = sin(2?) cos(2?)

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Q: 2 Let A = -1 1 3.) (AB) C -3 -5 5 -3 -4 B = 1 -1 3 -3 3 5 -5 5 C = 2 1 -2 3 -3 . Find:

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Q: L {cos nt}

A: Solution

Q: The circumference of a sphere was determined as 84 cm with a possible error of 0.5 cm. Estimate the…

A: A circle's or sphere's circumference is equal to 6.2832 times its radius. The circumference of the…

Q: 1. Let D= [-2,3) U {-3, T}. Determine the following: (a) max D, (b) inf D, (c) interior ED (a) b

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Q: a. Show that for every non-negative integers m, n, N = 7.5" has exactly (m+1)(n+1) different…

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Q: Suppose the pentagon below represents the base of a pentagon prism that has a height of 8 inches.…

A: We need to find area of pentagon and then multiply it by height to get volume of solid .

Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

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Q: Use variation of parameters to find a particular solution, given the solutions y₁, y2 of the…

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Q: D. Development 12 cm Find the area of each irregular figures. Write your answer 6 cm 6 cm 4 cm 7am 8…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

Q: Solve for y" (2): y" - y = 0, y(0) = 12, y'(0) =

A: Differential equation and it's solution

Q: Consider the system of equations: (a +1)x+ (2c-4)z = 2 -2by +z = 0 (-a - 1)x+ (1 - c)z = 1 Determine…

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Q: For each of the following, factor the matrix A into a product QDQT where Q is orthogonal and D is…

A: Q.10

Q: 3) Solve for y'" (1): " - 4y' + 3y = 6t - 8, y(0) = 0, y'(0) = 0

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Q: S L-²¹ {1²5²+7²7²} ; L and n

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Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: 5. For each linear system given, classify the critical (equilibrium) point (0,0) and use this…

A: We will find out the eigenvalues of the Jacobian matrix at the equilibrium point (0,0) to classify…

Q: 10. 1 -1 f(t) 3 1

A: Laplace transform of the function

Q: Exercise 1. Recall that a function f: ER is called Lipschitz if there exists M such that |f(x) =…

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Q: L {sin(wt + O)}; w and O are constants

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Q: Find an equation for the conic that satisfies the given conditions. hyperbola, vertices (-1, -3),…

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Q: 2: 2x²y + 4xy + 3y = 0

A: Solution :- As per guidelines.

Q: Find the coordinates of the point P on the circumference of the circle.​ (Hint: Add​ x- and​ y-axes,…

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Q: A cylindrical can, open at the top, is to hold 700 cm³ of liquid. Find the height, h, and the…

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Q: 3x 3x Determine whether F(x, y) = e³ cos 3y i – e³ sin 3yj is a conservative vector field. If so,…

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Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. P 3.f(t)= te2t sint IMAL

A: We need to find Laplace Transform of ,  ft = te2t sin2t That is , Fs = Lft. Fs = Lte2t sint We know…

Q: Higher Order Differential Equation Solve the differential equation: (D^2 - 1)y = (2)/(1+e^x)

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Q: 7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is…

A: Given that u is the unit vector in ℝn and H=I-2uuT . To Show: (a) H is symmetric.               (b)…

Q: 2) Solve for y" (2): " - y = 0, y(0) = 12, y'(0) = 0

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