Use spherical coordinates to evaluate the triple integral x² + y² + z² dV, where E is the ball: x² + y² + z² ≤ 4. E

Q: 1. State the amplitude, period, and phase shift for y=2 sin(0+20°). Then graph the function.

A: Given function is y=2sinθ+20°. We have to find the amplitude, period and phase shift of the given…

Q: fleax s [[e-8x sin(6x)] dx *Using the formula Evaluate ax sin(bx)] dx = 1 (a² + b²) eax [a sin(bx) —…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

A: # A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than…

Q: 8. Use Green's Theorem to find the area of the region enclosed by one arch of the cycloid: x = t -…

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Q: Exercise 15.2.17. Use Exercise 15.2.16 to prove the following proposition: Proposition 15.2.18. The…

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Q: H-w.4 Find the volumes for the following solids whose heights are defined by ZCx,y) and bases are…

A: To find volume for the solid whose height is defined by z(x,y) and the base is the region bounded by…

Q: 1. Find the general solution of the system of differential equations d -37 -56 26 -X = x+e4t ) dt 30…

A: Consider the given system of differential equation, ddtx=-37-563045x+e4t26-19 Compare with the…

Q: Compute the least-squares error associated with the least-squares solution x of Ax = b. 1 4 2 1,035…

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Q: 4) Determine the equation for the shortest arc that passes through the point (0, 0) and (1, 0) and…

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Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: Utt = 8urr x>0 u(0, t) = 0 u(x,0) = 1 u₁(x,0) = 0

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Q: Q1: (B): sketch the following waveform in(degree, radian, and time) abscissa 10sin (377t +30°)

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Q: You have answered 2 out of 4 parts correctly. Find the eigenvalues A₁ < A2 and associated unit…

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Q: Use the graph of the function f(x) shown below in order to determine lim_f(x). x-5 -10 -9 -8 -7 -6…

A: We want to find limit of given function when x tend to -5.

Q: Consider the following data X 4 5 6 7 f(x) 0.6 .65 0.74 0.78 Use forward difference formula of order…

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Q: Find all the values of a such that the given series would converge. Answer: Note: Give your answer…

A: Given series is ∑n=1∞xnn+4

Q: Find the nth Taylor polynomial centered at c. f(x) = In(x), n = 4, c = 6 P4(X) =>

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Q: The matching game is played in a bipartite graph G = (V₁, V2, E) in which edges are connect only…

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Q: Find the nth Taylor polynomial centered at c. f(x) = ln(x), n = 4, c = 6 P4(X) =

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Q: (c) Consider the system x'(t) =ay² - x, y' (t) = -y-ax². x' (t)-y-2x, y'(t)=2x-y-x³.

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Q: Find the general solution to the following equations. 1. x²y" — (y')² – 2xy' = 0

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Q: A hole of radius 1 inch is drilled through the center of a spherical wooden ball of radius 3 inches.…

A: To find the volume of portion removed by drill.

Q: Determine the Laplace transform of the following function

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that p≥ 5 is prime. Show that -3 is a quadratic residue (mo p) if p = 1 or 7 (mod 12) and a…

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Q: Cosx 2) ). y dx+ týž - Sinx (²) dy = уч

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Q: Z=Sn (PUS) n(QUS) NPNQNS

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Q: For all positive values of a,b and c, determine the equilibrium points of the system * x1 = ax1 -…

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Q: 1 Let f(x) x² (a) Let = (1, 0). For all p = [1, ∞], evaluate ||f||LP (M). (b) Let = (0, 1). At what…

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Q: 3.27.2. Let X be a metric space with metric d; let ACX be nonempty. (a) Show that d(x, A) = 0 iff x…

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Q: Test the series for convergence or divergence using the Alternating Series Test. 8(-1)"e-n n = 1…

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Q: Compare the functions shown below:   g(x) f(x) = 4x − 1   h(x) = cos(x + 2π) Using complete…

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Q: The value of China's exports of automobiles and parts (in billions of dollars) is where x = 0…

A: The function fx represents the exports.

Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cost) k…

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Q: (h) Suppose that G is an unconnected graph that consists of 4 connected components. The first…

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Q: Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 5i and corresponding eigenvector * =…

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Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: r(t) = (7t cos t-7 sin t)j + (7t sin t + 7 cos t) k OT= (-7 sin t)j + (7 cos t)k OT= (-sin t)j +…

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Q: 10. Prove that 7/2 TC/2- sin 0 cos (cos a cosec 8) de -0 2 (1-cos a).

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Q: Suppose that u, v, and w are vectors such that Evaluate the given expression. u-v-2w, 4u+vi (u, v 2,…

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Q: Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum…

A: Given: Properties of the function, To find: Label all the intercept points, relative extremum…

Q: How. Find the volumes for the following solids whose heights are defined by E (x,y) and bases are…

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Q: Solve (ut)² + (Ux)² = 1

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Q: ify and sketch the

A: Given,       9x2+25y2-16z2=0

Q: Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph…

A: To find slope of normal of f at point x=4 from the graph of its derivative.

Q: • Evaluat the integral:- 푼 S S. seč (cosx) dx dy Sin y

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Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

A: Instead of x1 , x2 , x3 i choose x,y,z We can solve this using gauss Jacobi

Q: 240 s+1)(s+2)(s+3)(s+4) C(s) Gls 70

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Q: log (x+3) 2+1-1-cosh (cos-¹x) lim

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Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*107 part/m³), while the…

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