X (c) √ √ ₁₂ √ a ² + y² dx dy if R is the region outside the circle x² + y² = 1 and within the circle (x - 1)² + y² = 1.

Q: 3.Find [, (3x² + y)dydx -2

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A: First, find the auxiliary roots from the given equation. Use yx=c1y1+c2y2 to write complementary…

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A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

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Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: the extremum of f(x,y) = 7x²y² +5y² 9x?. +

A: Given that: f(x, y)=7x2y2+5y2+9x2

Q: J (2x+y) dx + (x+2y) dy L is circle of center (7,8) and radius 9

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Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: Let a, b ∈ N. How many multiples of b are there in the sequence a, 2a, 3a, . . . , ba?   please…

A: Theorem: Let a,b∈N and least common multiple of a, b is denoted by lcma,b, greatest common divisor…

Q: Find the extremum of f(x,y) = 6x²y² +4y² + 4x².

A:

Q: 2. f(x,y)= 2x + 6xy +y

A: Partial derivative

Q: Find the centroid of the thin plate bounded by the graphs of g(x) = x² and f(x) = -x + 30. Use the…

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Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.

Q: nd f(3x²+2y)dx- (x+3cos y)dy through the parallelogram with vertices (0;0), (2;0), (3;1) and

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Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

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Q: l, (2 Y - x ) dA,where R is the region of the first quadrant bounded by the circle x2 + y? = 4 and…

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Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

A: Solution :

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: When having a differential equations set, are there rules to know about the stability of the…

A: When having a differential equations set, are there rules to know about the stability of the…

Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: Suppose ƒ(x, y, z) = ln(5x² + 6y + 5z²). Find an equation for the level surface of f that passes…

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Q: Let S(x, y) = x² + y² – 2x – 16y + 10 = 0 be a circle and L(x, y) = x – 5y + 10 = 0 be a line.

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Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

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Q: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)], F = ▼ ƒ(x, y), and C is the segment of the parabola y…

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