(A) Find div (e grad u xf) at (2,1,0) where x-y and =(x²+1)i+sec¯¹(x² −y)j + 3y²z. k YZ 11=

Q: Find V × (V × F) if F(r, y, z) = xyj+ 6xyz k.

A:

Q: 1. Let F(x, y) = 25x³ + 120x²y + 192xy? + 102y³ – 300x – 450y. Find the following: | ƏF (i). OF…

A:

Q: (x, y) = (b) 1 1 (d) 1/2 Does not exist. (x, y) = Ty³ x² + y6 = Find limf(x,y) along the path x =…

A: We will find the required.

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: 2 4 2) f(x,y)=2xy- 5x? - 2y² +4x+4y – 4 Ans. f 3'3 0 local max. %3D

A:

Q: Find [2² Pex. 2 √²+ 3 1³ F(x f(x, y) = 5x + 3x²y² 3 √³ F(x, f(x, y) dx and f(x, y) dx = f(x, y) dy =…

A:

Q: xy If z show that: x- y

A:

Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

A:

Q: 3. Show that f(x, y, z) fxx + fyy+fzz = 0. = 1 x² + y² + z² satisfies the equation

A:

Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

A: Given: Fx,y,z=xy j+6xyz k To find the  cross product of ∇×∇×F

Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

A:

Q: Find fx and fy for f(x,y) = y In (x + 8y). II

A: Step 1:​f(x,y)=yln(x+8y)​Step…

Q: Find dt OA. ○ B. OC. O D. for y = (5t? - 4t)?. dt dy dt dy dt dy dt = 2 (5t² − 4t) + (10t − 4) =…

A:

Q: Let U(z, y) (2x +3)(y+5). %3D Select the correct expressions for Uz and Uy: (A). Uz= 2x+3. %3D (B).…

A:

Q: Obtain the GS of: 2 (Згу — 4у + 6) dz + (23 — ва? ? — 1) dy %3D 0 - a. x³y – 2x?y3 + 3x² b. x3у —…

A:

Q: 3. Let f(x, y) = x³ 3x² + xy +7 and u = 0.6i + 0.8j, then find Duf(1,-2).

A:

Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

A: Introduction :

Q: f) Given w=(x+y)/(z-3y) , Find dw

A: Total derivative

Q: FI = r Where f(r) = -i = 2xi – 3yj + zk So be it %3D div) grad(f) find

A:

Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

A:

Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

A:

Q: Find fx and fy for f(x,y) = y In (x + 8y). II

A: To provide what is best and to understand more about the students concerns for their studies.

Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by y=x², and…

A: The region R:

Q: The equations xy² + 8xzcos(u) + ye" = 16 and x³yz+xe" – 3u?v² = 9 are solved %3D for u and v as…

A:

Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz 0. dx fie +

A:

Q: 2. Let f(x, y) = 4x³y² + 3x²y³, find: (a) Vj (1,2) (b) f(1,2), where u = 17-17

A: (2)  Given that  f x, y = 4x3y2 + 3x2y3  (a)     ∂f∂x = 4y2∂∂xx3 + 3y3∂∂xx2       ⇒ ∂f∂x = 4y23x2 +…

Q: f(x, y) = iy² – x², P(1,4), v = 2i + j

A:

Q: 1 1 J(A) = ,T AX 2 i=1 j=1 =;(x1A11x1 + X1A12×2 + X2A21X1 + x2Az (A - yariable, X-parameter)

A: Given,      J(A)=12XTAx      =12∑i=12∑j=12xiAijxj      =12x1A11x1+x1A12x2+x2A21x1+x2A22x2where A…