8. Determine whether each statement is True or False. (a) {} = Ø (b) r€ {r, y, z} (c) {1} c {1,2} (d) ØC {1,2,3} (e) ACA (f) {r, y, z} C {x, y, z}.

Q: 1 Evaluate f fp2 f (x, y) dædy where f (x, y) (1+æ² + y²)?

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

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

A:

Q: flx)= X tah? (X) C 2. f"G) こ

A: We have to use the quotient rule , so we assume u and v and find u' and v'

Q: Evaluate xy ds, where C is describe by æ = 4t, y= 3t, 0 <t<1. Enter your answer as a number in…

A:

Q: Sketch the regien enclosed by the given curueS Y = xe*

A: Question- Sketch the region enclosed by the given curves: y = x2 e(-x) &amp; Y= x e(-x)

Q: Evaluate dx V In(8-x)) at x = 1. = 1.

A: We have to find: ddxln(8-x2)3   at x = 1.

Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). u = , V = (a) u. V 27 (b) 306 (c) 306 (d) (e) u u ||u||²…

A:

Q: 5.) Evaluate (x² + y² + x)dA where R= {(x,y)|1<x² + y² <4, x 2 0, y2 0}. %3D R

A: Area of the bounded region is A=21+(255 π/8)

Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

A:

Q: the origin 2 2 S (1-10²1) ² dx -1 2

A:

Q: Find curlF for F = xyz?i+ x*yz?j+ x*y?zk.

A: Given, F→=xyz2i→+x4yz2j→+x4y2zk→ Used formulas, ∂∂xxn=nxn-1

Q: What is WX? X WX = Submit U W 5

A:

Q: If F = ⟨F1, F2, F3⟩ what is div (curl(F))

A: F = ⟨F1, F2, F3⟩

Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j