Calculate [(ydx – xdy)] wherein y(t) = (2cos(t), 2sin(t)),0 < t < - 27, is an circumference that delimits the set K = {(x, y) € R²; a² +y? < 4}

Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: 2. Evaluate f (3x + 4y2) dA, where R is the region in the upper half-plane 15 bounded by the circles…

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D %3D x² +x – 6' has…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,…

Q: Use Green's theorem to evaluate Sc(y² + x³) dx +xª dy where C is the perimeter of the square [0, 1]…

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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Q: Find the maximum value of f(x,y,z)=D24x+18y+21z on the sphere x²+y2+z²=D49 256.324

A: Given query is to find the max value for f.

Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: Numerically integrate f(x) = x2 from a=0 to b= 2 using a multiple segment (n-2) trapezoidal %3D…

A: Trapezoidal rule  ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2)+2f(x3​)+⋯+2f(xn-1​)+f(xn​))whereΔx=b-an

Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: Find the absolute maximum and minimum values of f on the set D for f(x, y) = x² + y? – 2x, where D…

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Q: Find the equahion a Hhe tangent Lie FlX) =482- 5X +7 when R=1

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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Q: Among all rectangular boxes defined by the inequalities 0 ≤x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one…

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Q: Find the maximum value of f(x, y) = 3ry(9 – 45x – 9y) over the triangle with vertices (0,0), (,0)…

A: Maximum value occurs at critical points or on the boundaries of the triangle.

Q: use the trapezoidal rule to approximate use n=6 and h=1

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Q: The area bounded by the curve y= 3va and the lines z = 3 and T = 8 above the z- aris is square units…

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Q: |Use Green's Theorem to evaluate | -x'ydx+xy°dy where C is the boundary of the C circle x + y =16…

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Q: Q2 (33%): Evaluate ff, xy d,d, where R is the triangular region bounded by the axes of coordinates…

A: We will draw a region first, then find integrals

Q: 2人+人 2X PM the From Pi (x,,y,z,) to Pz (xz, Yz, Zz Prove that the Midpoint of the line Ssegment 12…

A: Let the 2 points in the line segment be,

Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

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Q: Show that if y is the boundary

A: To prove that if γ is the boundary of the trianglee with vertices at z=0, z=3i,and z=-4 oriented in…

Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

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Q: 1. Find the area of the part of the planer+ 2u + 3z = 1 that lies inside the cylinder x2 + y? = 3.

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Q: Provide inequalities for r and that precisely describe the region in the xy-plane bounded by the…

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Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: (d) | (3+ecos (0 sd AX ·

A: As per your query the solution of the problem (a) has been done in midpoint rule. For the solution…

Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Let C denote the positively oriented boundary of the square whose sides lie along the lines x =+ 2…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: i) Use the residue theorem to evaluate 2z+6 dz, where c is the circle |z – i| = 2. z²+4

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Q: Let R=[0,6]×[0,6]. Subdivide each side of R into m=n=3 subintervals, and use the Midpoint Rule to…

A: Given :  R=0,6×0,6m=n=3     MIDPOINT RULE:

Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: Q5. Prove that the circle {(x, y), z² + y² = 1} is not homeomorphic to the interval (–1, 1). 1

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Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

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Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

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Q: find the tayler Polymomiul! P3(x) for the function fex) = X at a=1,3

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