2. Use the Divergence Theorem to compute ffs F. dS for F = (xy, yz, x² z + z² ) and S the boundary of the box [0, 1] x [2,4] x [1, 5]

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Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: n What is the closed-form expression for the series 2 (k-2)², k=1 37 A + 6 n³ -n²+ 13 B 6 6

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Q: Write down the first four terms of the sequence given by x, = 3" + 2", starting from n= 0. X1 = X2 =…

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A: This question can be solved by applying the concept of unit tangent and line tangent at a given…

Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

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Q: Assume that f(x)dx = 3 and g(x)dx = -2, find the following: 1. Sf(x) + g(x)]dx = 2. S12f(x) – g(x)]…

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Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: sec'xdx

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Q: Find the solution of y' = 2(2x-y) which passes through the point (0, -1) the answer should be y=2x-1

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Q: x2- 2 (x+ 2)(x + 1)² x+2 (x + 1)2 x+2 (I + x) Option 1 Option 2 1 (x + 1)2 x+ 2 (x + 1)

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Q: d Find [r(t) · u(t)] and [r(t) x u(t)] in two different ways. dt dt r(t) = ti + 2t2j + t³k, u(t) =…

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Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

A: Solution is given below:

Q: im Y cosx tZx 7x¢ with squeze thearem

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Q: Determine the amplitude, period, midline, and phase shifts of the function. Then write the equation…

A: Given problem:- Determine the amplitude, period, midline, and phase shifts of the function. Then…

Q: 1. Find the particular solution of the differential equation that satisfies the initial conditions.…

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Q: 2 and common ratio Write down the first four terms of the geometric sequence with first term (Type…

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Q: Find the particular solution that satisfies the initial conditic (e* + eX), f(0) = 1, f'(0) = 0 2…

A: Here we have to find the particular solution of given differential equation.

Q: Let f (x, y) = e(8x-9y). Find the equation for the tangent plane to the graph of f at the point…

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Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

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Q: (45)ds。(特)"- sa (49) 48 (xs) 1-1

A: The given integral is (x2+5x) /(x+9)1/4.

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Q: +2x-15 Inkx + 51 -inlx- 31 +c In]x+51-Inx- 31+C Option 1 Option 2 |(x + 5)°| +C (*+5) +C *-3 Option…

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Q: Use the properties of the derivative and the given vectors to find the following. = ti+ 8 sin(t)j +…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e*, -6), g(t) = 5t + 6 %3| 을r(g(t)) = 《

A: Use chain rule

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A:

Q: 1. The study of integrals in calculus is motivated by the problem of calculating (a) the slope of a…

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Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

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Q: 2. Find the 11th term of the following geometric sequence. 4, 12, 36, 108, ...

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Q: Find the average value of f(x)= 4x - 5 from 1 to 3. ... The average value of f(x) = 4x - 5 from 1 to…

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Q: P1. 18. Which of the following is true? Select one: O a. AxB is the same as BxA O b. If vector A is…

A: Vector

Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

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Q: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=z, x=0, z=0 in the…

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Q: Help Homer design a cylindrical silo to hold the output from his pet pig Harry Plopper. The silo…

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Q: v (km/hr) t (hours) -b The figure above gives your velocity during a trip starting from home.…

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Q: f(x)= 3sin Vx' – 3x + 2

A: Solution:

Q: 5 x X LOS

A: Given: I=∫0πsin5x2cos7x2dx  ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

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Q: k(u) is a degree 3 polynomial with k(0)=-21.24 and zeros 4 and 3i. Find an equation for k with only…

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Q: What is the range of the function y=f(x) =2sin 57 A [-3,7] B B [-7,-3] В © [-7,3] D D [3,7]

A: We have to find range of give function.

Q: Find an equation of the hyperbola having foci at (3, -11) and (3, 7) and vertices at (3, -4) and (3,…

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Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

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Q: H.W (5) Solve the following differential equations of ay (6x-y+3)dx+(3y' -x-2)dy 6) Integration…

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Q: stimate using the trapezoid rule and Simpson's rule for et dx;n3D8 -2x+5

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Q: 2-2 +2)Xx+1) (*+1P Option 1 Option 2 1. (x +1) *+2 (x +1) Option 3 Option 4

A: This question is related to partial fraction decomposition, we will solve it using given…

Q: nvestigate the convergence of the following series. H.V 2n+5n 2) Σ-1 3n %3D1 1LJ!

A: We have to find out convergence