Evaluate + x² + y² dS where S is the helicoid: r(u, v) = u cos(v)i + usin(v)j + vk, with 0≤u≤ 2,0 ≤v≤ 2π

Q: S(z,9) = z² + y*;z = f + P;y =P +° , % att = 1 equals Select one: Oa 0 Ob -1 O. 164 Od. 64

A:

Q: oWhich of the following clifferential equation s is Separable? dy A. e B. dã C. d - Sin Cay) %3D D.…

A: Explanation of the answer is as follows

Q: 2) O) by use chong of variables find

A: we have to find the following Integral

Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

A:

Q: Please don't provide handwritten solution ...

A:

Q: For the function of two variables defined by ƒ(u, v) = u² cos v + v² sin u, select the option that…

A: Given: Let consider the function of two variables, f(u,v)=u2cos v+ v2 sin uWe have to find ∂f∂u…

Q: Consider the exact U (x,y) that 2x + f = x taf Statistics. au aa au DDE (2x+ f) dx + (x + ² f) df =…

A:

Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: Gixen dw wt 3y x dt dy +2X +3 x Find the gencral oludtii, usri eign.

A: Write the given system into matrix equation as follows.

Q: Be w = (u2 + v2)3/2, where u = e-t sin(θ), v = e-t cos(θ), calculate: ∂w/∂t and ∂w/∂θ

A:

Q: Compute u X v and v X u for u = jX k and v = kX i. u X v = V Xu =

A:

Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

A:

Q: ди ди. Use the Chain Rule to find and др Ət = x2 +yz, и = x = r sint, = r cost y=

A: By using chain rule to find ∂u∂r and ∂u∂t. u=x2+yz, x=r sin t, y=r cos t

Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D…

A:

Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 9 cos(5x – 6y)j+ 10zk.

A:

Q: Integrate: S dx 5+ x2 5x

A:

Q: VX intersects XY at point Z. True False P

A: To determine whether the following statement is True or False. intersects  at point .

Q: Find rsint V1+ u+du) dt. dx2 Jo

A: We have to use the formula  Here  We write the second derivative as two derivatives and use f(t)…

Q: 7. Let f(x, y) = 2, where x = 2 cos u and y = 3 sin v. Find fu(x, y) and f(x, y) and y exprees them…

A:

Q: 2: find fr, fy, and fz.

A: Given fx,y,z=e-xyz to find fx differentiate with respect to x fx=e-xyzyz

Q: 3. Let f(x, y) = x sin xy. Find: (a) fæ(x,y) (b) fy(x,y) (c) fyy(x, y) (d) fyæ(x,y)

A: From the given function: fx,y=xsinxy As we know that: The chain rule: fgx'=f'gx·g'x The product…

Q: dw at (u, v) = (2, 5) for the function w(x, y, z) = xz + yz - z where x = uv, y = uv, z = u.…

A:

Q: n Evaluate : [(x + Vx? +1)" dx. X

A: