(3) For each region shown below, decide whether to use polar coordinates or rectangular J₁² f dA as an iterated integral, where fƒ is an arbitrary dxdy = rdrdo, and f(x, y) = coordinates and write continuous function on R. Remember that dA f(r cos(8), r sin(0)). (a) (b) -1 4 1 4 y=1-x² 1 X X (c) (d) = -1 У4 1. 0 6 1 X

Q: Calculate dw/du and dwldv using the following functions: = f(x, y, z) = 3x² – 2ry + 4z2 = x(u, v) =…

A: Apply chain rule

Q: - Let f(x, y) =sin(x y − x − 3y+3). (vi) Which of the surfaces below is a graph of this function?

A: Given .This can be rewritten asOn the xy−plane, , if  gives us hyperbolas on the xy−plane.

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

A:

Q: fyx if f(x, y) = sin(xy) + x² In y

A:

Q: 7. Consider the curve x = 3t + 4t3 + 100, y = 3t - t3, -2 <t< 2. dy What is dy when t = 1? dx (a)…

A: Let's find.

Q: dy (1 + æ)* Find for y dx Ans=

A:

Q: Evaluate 6z ds where Cis the curve y = -72² from (-1,-7) to (1, -7). Enter the scalar line integral…

A: To evaluate ∫C6xds where C is the curve y=−7x2 from −1,−7 to 1,−7.