2. Find the V.A and H.A r(x) = 2+2x+3 x2-5x V.A- H.A-

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: b) V = P,(R) B= {1,1+x,1+x+x²,1+x+x² +x'}; p(x)= 4-x+x² – 2x

A: Please see the below picture for detailed solution.

Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

A:

Q: I. If g(x) = Vx – 4 and h(x) = x³ + 4 , find (hog)(x) %3D

A:

Q: F= [y°, 2², x²], C : r= [3cost, 3sint. 2t], 0 < t < 4n

A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

Q: Find the value of c such that S xe = 3.

A:

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 5u − 2x = 3v + w

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

A:

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=&lt; 3x2y-z, xz3+y4, -2x3z2 &gt; To Find , grad divV  Let  V=&lt; V1 ,V2 ,V3 &gt; On…

Q: Find Duf at P. 2 + 2. 5,3 4 f(x, y, z) = 6x³y°z*; P(1, – 2, 1); u = Duf i

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Q: S6xw, fx,w (x, w) = 0, 0sxs 1,0 < w s Vã otherwise (3x2, fx(x) = lo, 0<x<1 otherwise

A:

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: 3. The value of k in the variation models y = kx and y = is called the of

A: The value of k in the variation models y=kx and y=k/x  is called

Q: O Find the linearization Lcx) for fex) 3x -8x+7 when a=

A: We will find the linearization L(x) for the given f(x)=3x2-8x+7 when a=-2 in the following step.

Q: 3 - If h(x, y) = y - xy – x2, find at the point (2, n) ду а) - 2.5 b) 7 c) -2 d) -1 e) 0 f) 1 g)…

A: Given that h(x,y)=y-xy-x^2

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

A:

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

A:

Q: d.A, A = {(x; y) E R² : y € [0, 1], x € [y², e-]}

A: Given: I=∫∫A1x34dA   A=(x,y)∈R2: y∈0,1, x∈y2,e-y

Q: #X-N, (M. E) where QX)-2X +3X;-2X,x, Find M.

A:

Q: Let f(z) = kz5 + az³ + cz. Find u(x,y) if z = 3.3 + 7.8i, a = 7, c = 11, and k = 3.

A: This is a problem of complex analysis.

Q: f (x, y, z) ) = x² + y² + z²; x* + y* + z* = 1 2. 4 || ||

A:

Q: (c) Will it always be true that W C X f(W) S (X)?

A:

Q: 9. For what value(s) of h will y be in Span{v1, V2, V3} if V1 = V2 = -4 V3 = and y = h

A: We have to solve given problem:

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: y = Vx + 3, y =x + Mx My (x, y) =

A: For calculating these values we have to calculate an area and for that we have to plot a graph.…

Q: Show that A Yk= V' Yk+r

A:

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: 1. y = x², y = vx, x=7 x = 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Q4\ If A(x,y, z) = 3x²i + 3zj – 3xk find the Div (Grad A). %3D |

A: Explanation of the answer is as follows

Q: - show that; L-1[e¬v$] = e %3D 2tynt

A:

Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

A:

Q: a2z + əx2 a²z If z = In(x? + y²), find ду?

A: Find ∂2z∂x2+∂2z∂y2.

Q: If u=2x+y and v=x-2y then the st ream line is y? x2 2xy+ 2 %3D

A:

Q: -v-S vdu G) - S -r lee) dx 2 (보라2) 2 (x²t2) - x2 2 (R?+2) ㅜ 2 (x? qz) - (x? $2) z (? t2) In Ix? tz…

A:

Q: o Find the Vf at the given point 2. (x,y.2)=(x² + y² + ²)² +In.xyz,P(-1,2,–2)

A:

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: x+y Show that: B(x+1, y) = B(x, y)

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: - find x, y z Select one: а. X-3,у-2,z-1 b. x=3,y=-2,z=1 С. X-3,y-2,z-1 d. x=3,y=2,z=-1

A:

Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 2xe³j – 3ek. - V·(V × F) =

A:

Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: C (7,1) and r = (x - h)2 + (y – k)2 = r2 O 0 = 1 + A+ X(q+ zA + zX

A:

Q: 11 f(x,y) 3x-7y+2, R is the rectangle with opposite car- ners (-1,0) and (1,3).

A: 12. Given: fx,y=2x+2y+2 and triangle with corner 0,0 To find the area of the triangle. The formula…

Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: Find the volue of im x3+2 the Val using 3. X-> hospital cule.

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Q: f(L,K) + x [loo-PeL-Pak] max dQ

A:

Q: 4. f(r, y) = + y + xy,find fay and fyz

A: Solve the following

Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

A: