|-4 Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. I. $. (x – y) dx + (x + y) dy, C is the circle with center the origin and radius 2 -

Q: 2e Let f (2) Let C be the circle (z – 4) (z – 6) z = 8 in the counter-clockwise direction. - - Find…

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Q: Evaluate the line integral f3y² dx + z² dy + (16 - x²) dz over the quarter of the circle of radius 4…

A: Kindly refer to Step 2 for the solution.

Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: Find F. dr for given F and C. (a) (2,4). F = −y sin(x)i + cos(x)] and C is the parabola y = x²…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: (x² + xy) dx + (y² - xy) dy; C: the line y = x from the origin to the point (2, 2).

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Q: a [2x – y 2.x dx [x +3y.

A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: B- Find the area of the surface generated by revolving the curve y = √2-x² about x-axis

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Q: SHOW COMPLETE SOLUTION, MAKE THE SOLUTION CLEAR. THANK YOU!

A: Step 1: Step 2: Step 3: Step 4:

Q: Evaluate f (3x²y — y²)dx + (x³ - 2xy)dy, where C' is the parabola y = x²/4 from the origin to (2,1).

A: The given problem is to evaluate the given line integral of vector field over the given path C is…

Q: Find the Zero and its oodex for the function flz)=1- Ti+Z+

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Q: Find the equation for the tangent plane to the surface -3x+ 9y -7z = -26 at the point (1,-1, Lütfen…

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Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…

A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²)) 3+ (3x+4y+6e²²) k (a) Find curl F. curl F = (b) What…

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Q: a- Find the limits of the functions below: 7x3 - limx→0 3-3x²-6x x+2 limx--2 Vx²+5-3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: c. Evaluate f 3x ds, where C consists of arc C₁ of parabola y = x² from (0,0) to (2,4), followed by…

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Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

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Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y? + 6, (1, 3, 16)

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