Evaluate the flux integral J Fon dA when S F = (0, sinh(z), cosh(x)) and $ 1/2,₁05 y≤5,220} 3 S = {(x, y, z) = R² | x² + z² = 4, 0≤x≤

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: let X~beta(a,b). find m.g.f ofY=ln| 1-x

A:

Q: Assume that V (x, y) is a global Lyapunov function about the origin for the…

A: The objective of the question is to understand the concept of a global Lyapunov function and how it…

Q: If h(X) =n) 3+3F(X) where FC1) =7 and f'(1) what is h'LI) ?

A: If h(x) = 3+3f(x)   where f(1) = 7 , f'(1) = 2 differentiate h(x) with respect to x.   then put x=1

Q: 5. gl1) = Cot3x ら。 -- HQ) = I+ Sin x 1- Sin X

A:

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

A:

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Consider y = xe^x on the interval [-5, 0]

A: In order to find global minima of the function, check the values of the function at end points and…

Q: Find the limit of the sequence. {v5, y5v5, V 5V5V5...}

A: Given sequence  5, 55, 555, …. We have to find its limit.

Q: Calculate the gradient of the following function fox, y) = (x – 2)^3 sin y, at (0,0]

A:

Q: S(x,y) =-x' +2x*y-² -4y+12 ED CALC

A:

Q: integral f t^3 In t dt

A:

Q: dx Cane:2e-25x

A: 13)

Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

A:

Q: H.W: find dz and əz | ди ὃν z = 4e* ln y, x = ln(u cos v), y = u sin v as functions of u and vif:

A:

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: Let f(x, y, z)= exy sin(x+y) Calculate fxxz· z²+1

A:

Q: find fsub(x), fsub(y), and fsub(z): f(x,y,z)=e^yz+sinx)

A: Given,          fx,y,z=eyz+sinx

Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

A:

Q: Let f(x) = 6 – x j'(z) = Preview

A:

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

A:

Q: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given :  F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2  H = (t ^ 5)/(1 + t) * i + 4t…

Q: Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z = 0 and…

A:

Q: (a) Compute P[(X = (1/2)]

A:

Q: Show that f(z) = x³+i(1−y)³ is differentiable only at x = 0, y = 1 and f'(z) = 0.

A: