4) Verify that Green's theorem is true for f,xy?dx – x²ydy ,where C consists of y = x² from (-1,1) to (1,1) and the line segment from (1,1) to (-1,1). Also evaluate SoV1 + x³ dx + 2xy dy where C is the triangle with vertices (0,0), (1,0) and (1,3).

Q: Draw the contour curves for h (x, y) _y²+x² -1+2x and c = 0, 2, 4.

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

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A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: Let Compute dw Əs dw Ət -(-3,-4)= -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A:

Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

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Q: Let Compute θω Əs δω Ət -(-3,-4) (-3,-4)= = w = -5xy + 4yz - xz, x = st, y = est, z = t²

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: y 2+ 1+ (A) (3,1) (B) (2,1) (C) (2,-1) (D) (1.5,0.5) (E) (1,0) 0 -1 P 2 3 Q(3,2) In the figure…

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Q: Find Vf(a), given the following data. Calculate 91, 92 and g3 such that Vƒ(a): 91 92 93 = || || = 91…

A: The given problem is to find the grad f for the given data of directional derivative of function f…

Q: Let Compute θω Əs δώ Ət -(-3,-4) -(-3,-4) = w = -5xy + 4yz - xz, x = st, y = est, z = t²

A: By chain rule, we will solve the problem.

Q: The roots of the characteristic equation of y"-7y=0 are:  a. √7.-√7  b. 0, 7 c. 7,7 d. 7.-7

A: Here I am attaching image so that you understand each and every step.

Q: d²y and dx2 Find dy then simplify whenever possible. dx 1) y = 3t5 – 2t x = 4t3

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A: We have to find

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A: The function which can be expressed in the form of Y=aX+b is called as a linear function.