Verify Green's Theorem by evaluating both integrals aN aM y2 dx + x2 dA ду ax for the given path. C: rectangle with vertices (0, 0), (5, 0), (5, 8), and (0, 8) y2 dx + x2 dA %3D ax ay

Q: Find the area of the shaded region. (2,7) (0,3). 26 2/3 2/3

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1…

A: The given equation of the curves are: y1=x2-3xy2=0 And the bounded region is as shown below: Now…

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A: Given the differential equation is (x + 2y - 1) dx + (2x + 4y - 3) dy = 0; when x = 2 and y = -1.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) 2…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = V x2 + y2 + z? (8,…

A: Gradient of function fx, y, z=x2+y2+z2 at  point 8, 7, 3

Q: Find the gradient of the function at the given point. Function Point F(x, Y, z) = Vx + y² + z? (8,…

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Q: Find r'(t), r"(t), and r'(t) · r"(t). r(t) = (t2 + 9t)i - 4t²j (a) r'(t) (b) r"(t) (c) r'(t) · r"(t)

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Q: Find the area of the shaded region. r = Vcos 20 r = 10 cos e NOTE: Enter the ezact answer. A =

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Q: Find the solutions of the system of inequalities by graphing: x + y 1

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Q: (a) Find the area of the region bounded below by the curve y = r² and above by the line y = 4 (b)…

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Q: 3t e2t dt Evaluate the following integrals. 4 Зе + - 5t5/2 a dt - t3 2x cos(9 - x2) dx sin(9 – 2) -…

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Q: y" +y' + 1.25y = 0, y(0) = 3, y' (0) = 1.

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Q: Find the second derivative of .2 y = Vx² + x-3 O 6/x^2 O 12/x^3 O 6/x O 12/x^5

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Q: dy 2 Solve (x2 - 1)+ 2xy x2-1

A: (x2-1)dydx+2xy = 2x2-1dydx+2xx2-1y=2(x2-1)2this Diff eq is Linear Diff Eq.dydx+P(x) y =…

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Q: Let A = (1,0, 2) and B = (6, -2, 3). Solve for projĄB.

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Q: Consider the following. u = (-2, 5, 4) v = (0, 1, 7) %3D Find u x v. Determine if u x v is…

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Q: _13. What is § 2sinx cos x dx? cosx A. In2 +C В. C. +C +C D. In2 _14. Which of the following has…

A: We use the method of substitution to  solve the given differential equations

Q: Evaluate: 5° (-0.45)'(-1)10+i 212- 3D1

A: The given expression is: ∑i=1∞-0.45i-110+i2i2-i We can rewrite this as: =∑i=1∞-0.45i-110+i2i2i…

Q: Evaluate: Σ 1°e(2+x)i+2x

A: The given expression is: ∑i=0∞1i!xi1ee2+xi+2x. We will use the fact: 1e=1 to simplify it. So it…

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A: This is a problem of differential equation. Solution consist of complimentary function and…

Q: ꭍkg(x)dx=___ where k is a constant * a.(k/2)ꭍg(x)dx b. ꭍg(x) c. kꭍg(x)dx d.1

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Q: Knowing that harmonic series is divergent, which of the following series is also divergent by Limit…

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Q: A tin can has a base diameter of 10 cm and a height of 10 cm. The can is initially full, but a hole…

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Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

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Q: In the differential equation (1 + 3x sin y)dx - x2 cos ydy = 0 , we let the substitution w =…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y,…

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Q: a L. determine whether the series Use the Integral Test to 2 Σ n=1 (2n – 1)4 is convergent or…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t=0 T(0) = N(0)

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Q: A rotating light is located 12 feet from a wall. The light completes one rotation every 5 seconds.…

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Q: The polynomial of degree 4, P(x)P(x) has a root of multiplicity 2 at x=4x=4 and roots of…

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Q: 1.lf f(x) and g(x) are continuous functions, then SIF(x) ·g(x)] dæ S f(x) dæ · ƒ g(x) dæ. 2.lf G(x)…

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Q: Let y = tan(4æ + 5). Find the differential dy when a = 5 and da 0.2 %3D %3D

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: (y + 1)dx + (4x - y)dy 0

A: Explanation of the answer is as follows

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Q: 8. - Evaluate | 1 dx 1+x а. d. none of the choices b. 1/ 2 е. -co с. f.

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Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

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Q: Evaluate c (xy+y+z) ds along the curve r(t) = 2ti + tj + (2- 2t)k, 0Sts1. (xy+y+z) ds=| (Simplify…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t²j dt

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