Example 1:- if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)-1 a(x, y) a(u,v)

Q: Find the Jacobian a(x, y, z) a(u, v, w) for the indicated change of variables. If x = f(u, v, w), y…

A: x=ρ sinφ cosθy=ρ sinφ sinθz=ρ cosφ

Q: 1. (J · K) v (~ J. ~ K) / :. J = K

A: There are three expression in the given logical statement. They are J.K ~J.~K J≡K We prove the two…

Q: 5. Let z1 = a1 + b;i and z2 = az + bzi. (a) Find Im[z,Zz + (Z)? – 2,7 ]. (b) Prove that (z)² = z,² .

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: W (s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(3, v:(3, – 2) = 7, F.( –…

A: Let's find.

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

A:

Q: U= {f.g, h, p, q, r,x,y,z) A={f, h, p.q.r) B={q, r, y, z) C={g, h, p.q.y} Find Cn (B'UA). Write your…

A: We are given 4 sets U,A,B,C. We have to find C intersection (B` union A). This is an elementary…

Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: Let W(s,t) F(u(s, t), v(s, t)) where u(1,0)-4, u,(1,0) 3, u(1,0)- 5 v(1,0) 7, v.(1,0)=-3, v(1,0)--6…

A:

Q: Thescalar componentof the projection of u= on to v=is comp(subscript v)u

A: This question is based on vector properties.

Q: (L[u],v ) = ( Au, v)) = (Au)"C v = u"A"C v, (u,L*[v]) = (u, A* v) = u"MA* v. (9.5) Comparing these…

A: Given: Lu,v=Au,v=AuTCv=uTATCv u,L*v=u,A*v=uTMA*v   To prove: A*=M-1ATC

Q: Compute u x v. (a) u =i-j+ 2k, v = 3i +j+2k (b) u = 2i + j – 2k, v = i+3k (c) u = 2j + k, v = 3u 4…

A: To compute: u×v. If we have two vectors A=x1i+y1j+z1k and B=x2i+y2j+z2k then: A×B=ijkx1y1z1x2y2z2…

Q: Find u ∙ (v × w)   if u = ⟨1, 1, 1⟩ , v = ⟨2, 1, 0⟩, w = ⟨0, 0, 1⟩

A: Given: u=1,1,1, v=2,1,0, w=0,0,1 we know that scaler triple product S.T.P. of given three vectors…

Q: f (x, y, z, u, v, w) 3æyzuvw + x²y²w? – 7cz° + 3yvw Calculate [af af af af af af + for a = y= z = u…

A: Solution

Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: af (8,9). Let f(x,y)=x?y*. Find ду

A: We are given: f(x,y)=x2y4 ⇒∂f∂y=x24y3=4x2y3

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(2, 6) F„(3, – 2) = 3,…

A: Consider the function of several variables Ws,t=Fus,t,vs,t It is given that, u2,6=3us2,6=-7ut2,6=9…

Q: Find af ?х af ду af дz af af 7 Әх ду ах af = = ду af = af дz f(x, y, z) = 3xy + 3xz - 3yz Find their…

A:

Q: Let u = u(x, y, z.) be determined near (1, 1, 1) by x²y³z²u³ + 2xy²u³ - 3x³z²u=0, u(1,1,1) = 1. Find…

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Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

A:

Q: Compute u X v.

A: Cross product of two vectors a x b is defined as a vector c, which is perpendicular to both the…

Q: 660. Let A = (1, 5), B = (3, 1), C = (5, 4), A' = (5,9), B' = (11, –3), and C' = (17, 6). %3D Show…

A: according to the problem, we have

Q: 3 For f(x,y) = In x+y°, 4,8)

A:

Q: Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = -2, u, (1, 0) = 8, ut(1,0) = -4 v(1,0) = -3, v.…

A:

Q: Let R (s, t) = G (u (s, t) , v (s,t)) where G, u, and v are differentiable, и (1,2) — 5, из (1, 2) —…

A:

Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: translation: 3 units up О гез,0), Л(1, ), К (0, 1) ТО, 3), Т4, 4), К (3. 2) T6, 3), J(-1, 2), K'(0,…

A:

Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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Q: Let u = (4, 1, 5), v = (2, 1, 3) and w = (-a, 2, a). (b) Find value(s) of a for which the angle…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.