Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check for agreement. F= (z-y,x, -x); 2 2 D = {(x,y,z2); + +1} y 9 12 8 2

Q: The cross product is anti-commutative. This means that axb=-bxa. Show this is true for a=(2,3,4), b…

A: Given  a→=2,3,4 and b→=-5,-4,-3. We have to show that  a→×b→ = -b→×a→.

Q: 2. Given Taylor polynomial is p₁ (x) = Σ;=1−¹)²(x − 1)³, compare log (x) and its (-1)-1 Taylor…

A: Concept: Let f be a function whose first n derivatives exist at x=a The Taylor polynomial of degree…

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. (2423-4x) dx = [

A: Here we will solve the indefinite integral,

Q: Find a vector with initial point (-4,-2, 1) and terminal point (-12, 5, -8). Then find a unit vector…

A: Given problem:- Find a vector v→with initial point -4,-2,1 and terminal point -12,5,-8.Then find a…

Q: •y+1 Q5. Evaluate S₂ S¹¹ xy dx dy. -2 Jy²

A: Topic = Integration

Q: The function f is shown below. What is the value of nswer in simplest form. -8 -3 N 3 H N W 4 in -5…

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Q: O Use 1st and 2nd derivatives, sketch the graph of given function 2x x² - 1 f(x) =

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Q: Use cylindrical coordinates to calculate: Sw(x² + y²) dV = [[[_x² + y²³ av W: x² + y² ≤64, 0≤ z ≤ 16

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Q: 3x³-28x² +40x-42 3x² - 4x+5 dx

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Q: B A 876, 5432 -10-9-8-7-6 -54 -3 -2 -1 1234 -1 Graph of f D 1 2 3 4 5 6 7 8 9 10 C x.

A: We will find the required.

Q: Evaluate: (In x)² x -dx - +C

A: Topic - indefinite integral ∫xndx=xn+1n+1+C

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Q: Evaluate £¹₁7 x8 − 7 x³ + 7 x² dx. Round your answer to two decimal places. £²₁7 r8 − 7 x³ +7 r² dr…

A: Given definite integral is: ∫-11(7x8-7x3+7x2) dx

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Q: Use cylindrical coordinates to integrate f(x, y, z) = z over the intersection (i.e. all the volume…

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Q: Find the unit tangent vector to the curve defined by 7 r(t) = (5 cos(t), 5 sin(t), 2 sin² (t)) at t…

A: To find the unit tangent vector to the curve defined by r→t=5 cost, 5 sint, 2 sin2t

Q: Using logarithmic differentiation, find the derivative of e-3x √√2x-5 (6-524 f(x) =

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: The differential equation dy x-2y+3 ax 2x+3y-4 = is reduced to [homogenous or separable

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Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: In this question, consider the vectors 10 8 V1 ~- - ( ) - ~- - ( ) - - - () ---- () v2 = V3 = b and…

A: The objective of the question is determine the coefficient matrix" A" without simplifying.

Q: Find the domain and range for the function f(x) = LO T 5 3x 1- e

A: Find the domain and range of the function fx=51-e3x

Q: Find the first five terms of the sequence. 011/5 82=1/25 83 1/125 841/625 85 1/3125 50 Determine…

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Q: Consider points A(4, -1, 3), B(3, 1, 6), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

A: The given problem is solved below in detail.

Q: Devin invested an amount of $10,000.00 in a mutual fund. After 2 years and 6 months the accumulated…

A: The solution is given below

Q: How long will it take for an investment of $3000 to double in value if the interest rate is 6.5% per…

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Q: Find the mass of the surface lamina S of density p. S: z = √₂²x² - y², p(x, y, z) = kz ka+n 2 X

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Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: m M|L II k=0 CO M« Σ N சிய

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Q: Evaluate the indefinite integral. 5 fz¹ √8+zºdz + C

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Q: Find the area of a triangle PQR, where P = (-4, -2,-2), Q = (-5, 2, 5), and R = (-2,5,-4) Check…

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Q: Rewrite sin(x+ H Enclose arguments of functions in parentheses. For example, sin (2x). sir 20 in…

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Q: Find the radius of convergence for: (-1)"x" √n +7 n=1

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Q: 9. Compute the area of the region in the ry-plane wich is bounded by the z-axis and the curve r(t) =…

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Q: 5) Show that to order O(h²), the central difference formula for the partial derivative მ3u(x,t) əx3…

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Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Evaluate the triple integral g(x, y, z) dV over solid B. B = {(x, y, z) | x² + y² ≤ 10², x ≥ 0, y ≥…

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Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8 -7 -6 -5 -4 -3…

A: This question is related to definite integration, we will solve it using given information.

Q: Solve the differential equation dy dx y+√√x²+y² X O a. y² = 2x-1 O b. x2 = 2y-1 O c. √x² + y² O d.…

A: To solve the given differential equation.

Q: Find the Taylor Series generated by f(x) = (7 · X) ² at X=6 : f'(x) =__9 (7-X) 10 90 ƒ"(x)= (7-x)"…

A: The given function is fx=17-x9 centered at x=6

Q: 1.3: The derivative of the function sin(cos x) is a) cos(cos x) b) cos(-sin x) c) sin x cos(cos x)…

A: The given function is: fx=sincosx As we know from the Chain rule: fgx'=f'gx·g'x And the common…

Q: 9. Which of the following is f(x) = x³ the parent function for? a) f(x) = 8x³ - 13x + 11 b)…

A: 9. Which of the following is f(x)=x3 parent function for.

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

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Q: Let à = (1, -2, 0) and 6 = (1, 3,2). b Find the angle between the vector (in radians) Check Answer

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Q: 1. Conisder the vvf r(t) = 12ti — +8t³/2 j + 3t² k, t> 0. (a) Find the arc length of the curve for…

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Q: Evaluate f 4x²-3x+2 X dx.

A: Given, ∫4x2-3x+2xdx

Q: The function f is shown below. What is the value of answer in simplest form. -10 -9 -8 -7 -6 -5 4 3…

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Q: Find the arc length (s) of the curve (t) 8 = r(t) = (5e³t, 4e³t, 2e³t) for 0 ≤ t ≤ ln(4)

A: The arc length s of a curve r→t = xt, yt, zt for a≤t≤b is given by s = ∫abx't2+y't2+z't2 dt

Q: 3. Consider the following vectors: ä=7-2] +3k, b=27-3k, and a = -37 +2j. Compute the required…

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Q: Find the area of the parallelogram with adjacent sides u = (4, 3, 0) and v = (0, 3, 1).

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Q: Find the area under the curve y 2 I over the interval [1, 4]

A: Find the area under the curve y=2x over the interval [1, 4]