4. Find all local extremum of the functionf (x,y) = x2 – y2 bounded by the circle x2 + y2 = 1: %3D

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Q: S.(2x° +5y )dx+(2x-4y') dy C:boundary of the region lying between the graphs of x² +y² = 16 and x +y…

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

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A: Introduction: The formula of the area between the curves y=f(x) and y=g(x) is given by,…

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A: The region is bounded by the curves, The region is shown in the graph given below,

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Q: 5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x…

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Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curvex² = 4y %3D OA 3 О В.…

A: The shaded region shown in the figure is the area of integration

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A: To find the area of the following region :-

Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

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A: The solution is as follows

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

A:

Q: b. Evaluate the line integral ycos(xy)dx +(xcos(xy)+x)dy where R is the circle x'+y =9 traversed…

A: Solution Given b). ∫y cos(xy)dx+(xcos(xy)+x3) dyevaluate the line integral

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.

A: Plotting the Curves on X and Y-axis : y = x2 ...............(1)y = x + 2 ..............(2)After…

Q: 3. Let R be the region below bounded by the parabola y = 4x² and the lines 3x - 2y +3=0 and y = = 0.…

A: Follow the procedure given below.

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Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: (iii) Sf xy²e*dA, Dis bounded by y = x,y = 2,x = 0.

A:

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: Given (1 + y³)y' = x². (i) Determine a region of the xy-plane for which the given differentia…

A: Explanation of the solution is given below...

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Q: Consider the region bounded by the parabolas x = 8y^2 and x = 5 + 3y^2

A: Given parabolas equation-x=8y2  ....(1)x=5+3y2 ....(2)Solve equation (1) and (2) we get…

Q: Find the minimum and maximum values of: f (x, y) = x² + xy bounded by the graphs y = x´ and y =9

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Q: find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y + 1…

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Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curve y² = 4y %3D OA3 O B.…

A: To find: The value of ∫xydxdy over the region bounded by x- axis, ordinate x=2 and the curve x2=4y.…

Q: Determine a region of the xy-plane for which the given differentail equation would have a unique…

A: Given differential equation (y-x) y'=y+x   or    (x+y)dx+(x-y)dy=0 Note that differential equation…

Q: Find the absolute maximum and minimum of the function f(x, y) = 3y – 2x2 , constrained to the region…

A: f(x, y) = 3y – 2x2 , constrained to the region bounded by the parabola y=x2+x-1 and the line y=x.To…

Q: 4. Find the absolute maximum and minimum of the function on the given closed bounded region. y…

A: Given function is fx,y=ex2-4x-2y+y2 Closed region is x=0,y=0 and x+y=3 The objective is to find the…

Q: 3. Find the extreme values of the given f(x, y) on the indicated surface. f (x, y) = 8x² – 2y; x² +…

A: The solution of the problem is given in the next step.

Q: 5 Find the valume of the Sotids abtaind by-revelving the Yegion in the firstquadrand boundby the…

A: Sketch the graph and find the region. Using shell method, volume is evaluated.

Q: Let D be the region bounded by the parabola y = x2 and the curve y = sin x, and let P represent a…

A: If the input of the function is more than one, such functions are called multivariable functions.…

Q: 3. Let D be the region bounded by the parabola y= -3 and the line y=1.F

A: The region is bounded by the curves given by: y=x2-3      and      y=1

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Q: Let f (x, y) = y³ + x² – 3y (a) Determine all the critical points of f. (b) Determine the absolute…

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Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: For numbers 8 - 15: Let M be the region bounded by the parabola y = x² and the line y = x +2. y = =…

A: The objective is to find the area of the shaded region.

Q: Let h(x, y) = 2x² – 2x²y + y². Find the absolute minimum and maximum values of the surface on the…

A: We use partial derivative to find critical points to check maximum and minimum value

Q: Calculate fSp(3x + 2y) dA where D is the region in the first quadrant that is inside the circle x2 +…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Let f (x, y) = y³ + x² – 3y (a) Determine all the critical points of f. (b) Determine the absolute…

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