Evaluate ǝw (x, y, xz) ds where W = {(x, y, z) : x² + y² ≤ z ≤ 1}.

Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

A:

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: Evaluate [[ 4.ry² — 5x + 5y³ dA over the rectangle R = {(x, y) : -1 ≤ x ≤ 2 and − 1 ≤ y ≤1}.

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Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

A:

Q: VXVYP(x,y) is equivalent to VyVxP(x,y). O True O False

A: ∀x ∀y Px, y is equivalent to ∀y ∀x Px, y.

Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

A:

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

A:

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

A:

Q: 3. Let R= {(x, y) : x² + y² 0, y > 0}. Evaluate // Vz? + y² dA x2 +y? dA R

A: using polar coordinates x=rcos(θ)y=rsin(θ)x2+y2=r2,dA=r drdθ

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: Evaluate [², dx V4-x2 2.

A:

Q: Let X-(1,0,- 1,-V2). Then, |X|l3 = %3D Select one: a. 2+2/2 O b. C. 2 O d. arch

A: Answer :