6. Divergence and curl combinations (incl. identities) (a) Show that V. (fVg) = ƒV²g + Vf. Vg (b) Let f = zy + yx, v = (y, z, 4z - x)T, w = (y², z², x²) T. Find i. Vf and fVf at (3,4,0) T ii. V. (v x W) iii. curl(vx w) + curl(w x v)

Q: Find dy 2 2.

A: From the given problem:   x2y2=x2+y2   As we know that the Power law:   dxndx=nxn-1   Now…

Q: If A = A−¹ . 9 7 1 0 1 5 00 01

A: The matrix is given byTo determine: The inverse of the given matrix.Formula used:

Q: 2 -1 se s? +4 .2

A: Given:       L-1se-π2ss2+4 Apply inverse transform rule:       if L-1Fs=ft then L-1e-asFs=Ht-aft-a…

Q: Simplify. 10m n² 5mn4

A: To simplify the below expression.

Q: Simplify. v-7 2- 14v+ 49 ?

A:

Q: S t Vat²-b dt

A:

Q: Solution for h?

A:

Q: 7. Let ƒ(x) = 4x − 3, g(x) = x² + 4, h(x) = x + 5. Evaluate the following.

A: Given f(x) = 4x - 3 g( x ) = x2 + 4 h( x ) = x + 5

Q: 4. w/- 4. 2.

A: Given:

Q: A = 1 1 0 0 1 -1

A: Note the following fact :

Q: 0.4r-0.13-0.7r=3r-5.74

A:

Q: Evaluate. .3 S (-x² + 4x – 5)dx -2

A:

Q: Multiply. (ex − e−x)2

A: Here we multiply this:

Q: Write a triple integral which computes the integral of the function f(x,y,z) = xz over the region R…

A:

Q: Solving a System of Linear

A:

Q: (x, 5), (2, 6) m = 3/4

A: Let the equation of line be y=mx + b  ...(i) We have m=3/4 = 0.75

Q: .2 y = 4 - x² and x +y = 2.

A:

Q: Simplify. -16 6. 36 4 i 2 3 -4 4

A:

Q: Simplify. 7/16-V54

A:

Q: 4. %3D х+2 х-5 :- 3.

A:

Q: W X Y Exs. 4, 5

A: Given: mXW⏜=60, mWZ⏜=70, and mZY⏜=70.

Q: Steť?+1 dt

A: Let take t^2 = z  Then.differentiate it ansd solve it as. Below