1. Evaluate the following integral: (6 + 3 cos x) dx a. Analytically b. single application of the trapezoidal rule c. multiple-application trapezoidal rule, with n = 2 and 4 SITY

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A: We have to find the correct representation of the sum 5+7+9+11+13+⋯+101

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A: This is a problem of 3D geometry, and calculus.

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Q: Prove that the function f(x1,x2) = In (e*i+= + eV=i+1) is convex over R².

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Q: 7. What is Laplace [ tu (t-2)] ?

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Q: 4. (s+1)²(s²-4s+85)

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Q: What is the inverse transform of F(s) = In (s'/Vs2 +4s +5}

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Q: 7. Use the Euclidean algorithm to find the greatest common divisor of 142 and 3084.

A: By the Euclid division lemma If a and b be two positive integer then there exist unique positive…

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Q: Determine the Inverse Laplace Transform of the following: 4 3 1. + 52+4s+4 + s2+2s+2

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Q: Find a + b + c + d + e. The Fourier series of the function f(t) = i 풀 Stsnis: %3D 00 %3D cos 72…

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Q: Find the area of the shaded region. NOTE: Enter the exact answer. y = x2 + 2 A =| y = x 2

A: We want to find the shaded area.

Q: Find the inverse Laplace transform following: 0.2s+1.8 1. s+3.24

A: The problem looks difficult with decimal point but it isn't. Note that 3.24 = (1.8)^2 and so the…

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Q: 6. Let A = {1, 2, 3, 4} R = {(1,2), (1,3), (2,3), (2,4), (3,1)} S= {(2,1), (2,4), (3,2), (3,3),…

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Q: 2. Suppose that S is a surface in R3 with unit normal vector N surface area of S is given by (n1,…

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Q: Consider the following first-order ODE: dy 4e0.8x – 0.5y, x = [0, 1], y(x = 0) = 2 %3D dx The…

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Q: 1. The equation x² + y² = 9 represents a circle. Find the x-intercepts of its graph by letting y = 0…

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Q: The graph of a function f is given. 0 i 10 Estimate f(x) dx using five subintervals with the…

A: ∫010f(x) dx

Q: In this group of problems, you are given two statements, A and B: determine whether one statement…

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Q: If A has A1 = 6 with eigenvector x1 = and A2 = 4 with eigenvector x2 = |, use XAX- to find A. No…

A: Eigenvalues and Eigenvectors

Q: a) Yt+1 = 2yt - 10 b) Yt+1 = Yt c) ye = 0.5yt-1+1 %3D

A: This is the problem of recurrence relation.

Q: HwH Find the Volumes reights ae definedby ECX,y) and bases are the regiuns bounded by the falawng…

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Q: -2 4 -2-4 Let A= 2 -6-3 1 3 8 2 -3 a) Find bases for Nul A,ACol A). b) What is the dim Nul A)),^ dim…

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Q: True or False? If the functions Yı and y2 are linearly independent solutions of y/" + p(x)y' + q(x)y…

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Q: Calculate the Laplace inverse of 4s +8s 10. F(s) = (s- 2)(s² – 4s +13)²

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Q: Find the area of the region bounded by the x and y axes. the line x = 2. Show your complete…

A: Using double integral in Cartesian coordinates.

Q: 1. Suppose f e S(R) is an even function. Show that f is also even and that = f. (That is, f(€) →…

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Q: View Policies Show Attempt History Current Attempt in Progress Find the volume of the solid that…

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Q: - 3/ Sketch a sinusoidal function, f(x), that passes through (0, 4) and has a period of 24, an…

A: Here we have given that sinusoidal function fx passes through 0,4 and has period of 24, and…

Q: y -0.5 -0.75 1.5 0.5 0.25 -15 |(1) (2) (3) |-1.75 1.5 -0.5 0.5 0.25 -0.5 y y -0.5- 0.5 -이125- 0.5 -1…

A: Matched surfaces and contour diagrams:   Surface              Contour diagram (a)…

Q: Number of voters 9. 11 9 5 22 CBD B CA CDAC D A D B 1st choice D A 2nd choice B 3rd choice 4th…

A: Given Number of voters            9            11            9            5            22 1st…

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Q: Give the next number in the given series of numbers: 12, 28, 49, 75, 106

A: The given series is 12, 28, 49, 75, 106. We have to find the next number in the given series of…

Q: Verify the condition of integrability for the given total differential equatior (3x*y2 – e*z)dx +…

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Q: Use series to approximate the value of the integral with an error of magnitude less than 108. 0.14…

A: Given:∫00.14 sinxxdx

Q: 2. In a quadrilateral ABCD, ZA = 72° and 2C is the supplementary of ZA. The other two angles are…

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Q: 2. 1.5 sin(3t-

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Q: Calculate f(t), if given F(s) the following is s² +b? (4). F(s) = In (s - a)2 %3D

A: Inverse Laplace transferom

Q: Identify and sketch the graph of the given equation in R3. x2 + 2y2 + z2 - 8x + 12y - 2z + 35 = 0

A: We have to identify and sketch the graph of the given equation x2+2y2+z2-8x+12y-2z+35=0 in ℝ3

Q: (d) the equation of the line tangent to the curve at the point where (i) t =, and (ii) t = . = 17

A: We have x = 4sint,  and y = cost

Q: どY x=Jut Find dZ üs ing choin yule.

A: Solution

Q: 3. Solve the following IBVP: Ut = Uzz + sin(37x), 00, u(0, t) = u(1, t) = 0, t> 0, u(x, 0) =…

A: Solution

Q: How much is the maturity value if 14,500 is placed in an account earning 6.25% simple interest for…

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Q: 2. Determine the second derivative of f (x) = x'e* at x= -2 with a step-size of h=0.50 using Central…

A: Given function is  fx=x2e2x

Q: 2. Let p, q and r be the following statements: p: You run 10 laps daily. q: You are healthy. r: You…

A: Given that p , q and r are the following statements:                               p : You run 10…

Q: -2/The graph below shows the movement of a wheel spinning underwater Determine the speed of the…

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Q: Exhibit 1. Solver Sensitivity Report. A B C D E F G H 6 Variable Cells 7 Final Reduced Objective…

A: Given,Solver Sensitivity Report To find: Optimal objective function O(f).

Q: Find the general solution of the DE: y" + y" – 16y' + 20 = 0.

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Q: Prove the 2nd form of the mean value property: if ueC?(2) is harmonic, then u(x)= m(B(x,r)) u(y)dy…

A: As per the question we have to derive the 2nd form of the mean value property(MVP) for a harmonic…