Evaluate √√ √1 + x² + y² dS where S is the helicoid: r(u, v) = u cos(v)i + u sin(v)j + vk, with 0 ≤ u ≤ 5,0 ≤ v ≤ 2ñ

Q: . Use the I function to do the following: (a) find the value of SVxe*dx ,

A: We shall solve first question only as per the answering guidelines.if you want other question to be…

Q: For long cirular cfinder of Re two halves maintained at temprature U1 and Vi respectively, Show that…

A:

Q: Consider the function w = √√x² +: dw b) Find əs 6z where x = sinp, y=p+3t-4s, z = and p = 1-2t.

A: I have explained everything with in the solution. Please go through that.

Q: Q3:- Verify that the following functions u are harmonic, and in each case give a conjugate harmonic…

A:

Q: Find SS₂ cos (x² + y²)dA where D = {(x, y) | 4 ≤ x² + y² ≤ 36} D

A: Let's solve given double integral.

Q: Evaluate I = f. F. dr, where F(x, y) = (y + sin(x²), x² + e) and C is a circle of radius 5 centered…

A:

Q: y2 +Cos f (x, y, z) =

A:

Q: how that u(x, y) is harmonic in some domain and find a harmonic njugate v(x, y) hen: u(x, y) = 2x –…

A:

Q: Show that v(x, y) is harmonic in some domain and find a harmonic conjugate u(x, y) (7 Marks) When:…

A: XjjThis question is related to complex analysis

Q: а. Write the following complex function in the form of f (z). f (x, y) = sin x cosh y + i cos x sinh…

A:

Q: 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…

A: we have to find the surface integralfor the helicoid with For the given surface integral and…

Q: Find dz and ● dz de . || ab 11 ab for sin (a) sin (a) a da Ә f Әх sin (5x y².z) = 3 + 4x + 5y + 3z.…

A: We will do partial differentiation.

Q: Verify that the function u, defined by u(t, x) = t sin(x – t²), is a solution to the equation ,2 U +…

A:

Q: If f(x,t) = ²√ke-² dy, then prove that kfxx = ft.

A:

Q: az over the contour C |z = 4.5 sin z (b) Сompute

A:

Q: Find the lateral surface area A of the cylinder that lies above the xy-plane and below the surface z…

A: Given that the surface and is formed by line segments parallel to z-axisfrom the smooth curve:…

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

A:

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: dv (1 + v²)(1 + tan¬l v)

A:

Q: 95: Find W,e if W =f (x, y) , x =r cose and y =r sine, then prove that r W,e = -yfx+ xfy + xy(fyy-…

A:

Q: a) Given the velocity of a particle moving in space is v(t) = 3e² i + t2 j + 4 sin 2t k. Find the…

A:

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…