Use a triple integral over spherical coordinates to evaluate (2² + y²) dV, where E is the sphere a² + y² + z² = 1. 2 COS x - 3 sin? x cos x +C Hint: sin x dx 3

Q: 2. (a) Use the method of Laplace transforms to find the solution y(t) of the initial value problem…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Q-5: a) Find the area of the region enclosed by the two graphs y = e²x and y = 1-x, on [0,1]. b) L…

A: Sol:- aThe area between curves definitionThe area between curves is the area between a curve fx and…

Q: Find the average value of f(x,y) = x² + y² over the region R: rectangle with vertices (0,0), (2,2)…

A: Introduction:   A function f(x,y) average value as defined by favg=1A(R)∬Rf(x,y)dA   where A(R)…

Q: A parametrization of all the points on the sphere a + y² + z? = 1 that are such that y > 0 is given…

A: Find the parametrization of points on sphere x2+y2+z2=1, where y≥0. The equation x2+y2+z2=12…

Q: Approximate 22 dr with six intervals and the trapezoid rule.

A: The trapezoid rule can be defined as: ∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn), where h=b-aNand N is…

Q: 2. State the leading coefficient, degree, and symmetry. [K/U 6] a) y=3x-4x² +2 b) y: -6x c) d) (2,…

A: Degree of a polynomial- The highest power of the variable that occurs in the polynomial is called…

Q: Explain why there is no vector v such that × v =.

A: We explain why there is no vector v such that  <1,2,1> × v =<3,1,5>

Q: Use the given transformation to evaluate the integral. 3xy dA, where R is the region in the first…

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Q: 16. A flower farmer predicts that 85 % of the rose in the bushes he plants will grow rose buds that…

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

Q: a) The region R lies inside the curve r v2 sin 0 (for 0<0 <n) and outside the unit circle r = 1.…

A: We have to sketch the region R which lies inside the curve r=2 sinθ for 0≤θ≤π and outside the unit…

Q: Find the directional derivative Duf(P) of f(x, y, z) = x²y?z²at the point P(1, 2, 3) in the…

A: We have to find the directional derivative of f(x,y,z).

Q: Find the flux of the vector field F(x, y, z) = (yz, y°, xz) %3D across the surface S, where S is the…

A: Given

Q: Evaluate the line integral (2 - u) dz + (3 + æ) dy] where C is the parabolic arc = a² from (0, 0) to…

A: We have to evaluate the line integral.

Q: The figure shows the region of integration for the integral. 49 7-y f(x, y, z) dz dy dx Rewrite this…

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Q: needed to be solved correclty in 15 minutes and get the thumbs up please show neat and clean work…

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Q: Set up and simplify (but do not evaluate)/ F. dr, where F(x,y) (x2, xy), andC is the arc of the…

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Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: The solution is below.

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A: First we solve for critical point find the partial derivative with respect to X and y separately and…

Q: The graph of the function f is shown below. Which statement best describes the value of f'(-1)?…

A: Please see the below picture for detailed solution.

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

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Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: 2x+ 1 (a) A functionf has the property that f = x + 6 for all real values a # 0. What is the value…

A: a) The given function is f2x+1x=x+6 for all real values of x≠0.

Q: The figure shows a curve C and a contour map of a function f whose gradient is continuous. y 65 55 C…

A: Given,A curve C and a contour map of a function f whose gradient is continuous. To find: ∫C∇f.dr