Calculate the given quantity if u =i+j- 4k v = 5i - 2j + k w j- 3k. (a) 2u + 3v (b) Ju| (c) u. V (d) ux V (e) v x w () (v x w) (g) the angle between u and v (rounded to the nearest degree)

Q: Given f(x,y)=sin(x)+cos(y) and v a unit vector forming an angle of θ with the x axis. What must be…

A: We have to find  the value of θ, (with 0⩽θ⩽180 ) where the directional derivative ∂f∂v (0,π/2) to be…

Q: In Exercises 29–31, find the equation of the line tangent to thesurface at the given point P and in…

A:

Q: 3) If A = 2x²i – 3yzj + xz?k and ¢ = 2z – x³y, find A - Vo and A x V¢ at the point (1,-1,1). ww. 4)…

A: A=2x2 i-3yz j+xz2 kA(1,-1, 1)=(2, 3, 1)ϕ=2z-x3y∂ϕ∂x=-3x2y∂ϕ∂y=-x3∂ϕ∂z=2∇ϕ =∂ϕ∂x i +∂ϕ∂y j+∂ϕ∂z k∇ϕ…

Q: z = x2 + xy4, x = uv? + w°, y = u + ve" dz when u = 3, v = – 2, w = 0 dv then find:

A: Solve by partial differentiation

Q: = f(x,y, z) = x + sin y and Calculate if w ди x = x(u, v) = In (u + v), y = y(u, v) = e".º and z =…

A:

Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y & z considering other as constant at…

Q: Find (au / ay) at the point (u,v) = (√6, − 1), if x = u² + v² and y= uv. ди (2) (Simplify your…

A:

Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

A:

Q: Which of the following represents the distance between (X. (X2. Y2) O A. d = 2 / (x2 +1) + (y2 +Y1)…

A: Given two points, A(x1,y1) B(x2,y2) distance d=?

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

A:

Q: 5 Jlgu ntinuity equation satisfied by u= 3x^2-2y^2, v=-6xy IO 4xy+y?, v= 6xy+ 3y .II O U = u=x-4y,…

A: We have to solve given problem:

Q: 6.10. Prove that (a) J,"(x) = ¿[J,2(x) – 2J,(x) + J, +gl«]. %3D n-2

A:

Q: If V = (3x + 2z²)i + j- (z – 7x)k then V. V at the point. (1, 1, 1) is ||

A:

Q: 45. In AXYZ, W is between Y and Z. The coordinates are X(2,3), Y(5,0), Z(0,0) and W (2,0). What is…

A:

Q: X > U (M-, M+) M, Xca) 3. X(2) rimators: 2 1x

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: A particle moves in the XY plane so that at any time -2 <t<1, x = 5 sin t and y = t² – 3 cost – 1.…

A: NOTE: Refresh your page if you can't see any equations. . the horizontal component is x=3

Q: (c) Ã = xẽ, + yếy, C : {n² + y² = 1, z = 0} %3| ex (d) Ā = En + Ey 2 + 12 C : {y = x, z = 0, x € (0,…

A:

Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2u + 3v (b) |u| (c) u-v…

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3.…

Q: 2+i Evaluate (2x+1+iy)dz along (1-i) to (2+i) 1-i

A:

Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: If 0 < u < and x 2 sec u, then V x – 1 = f(u), where | f(u)

A:

Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

A:

Q: af Calculate at point (-1,2) where f (x, y) = 8+ x² + 3y? dv and v = i+j. 10 2 5/2 V2

A: fx, y=8+x2+3y2  &amp;  v=i+j Partially differentiating with respect to x, we get fxx, y=0+2x+0=2x…

Q: Find V· (V × F), if F(x, y, z) = e*²i+3xe'j – 7e*k. V . (V × F) = x z evz 三

A:

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: If f(x, y) = 3e-2x cos (y – 2), then the linear approximation at (0, 2) is (A) 3 – 3x (B) 3+ 6y (C)…

A: A function of 2 variables can be linearized using the partial derivatives. The formula for the…

Q: x+2 السؤال الثالث: جد ناتج التكامل (x - 4y + y* z)dydxdzباستخدام التحويل v =, u = 4y – x, W =

A:

Q: ( b) For n=1,2,K , show that (x² –1)y"*) +2(nx + p)y") +(n² –n)y"-1) =0 where %3D d" y p") = (Hint:…

A: * Given that y = x+1x-1pa dydx = px+1x-1p-1ddxx+1x-1    dydx = px+1x-1p-1x-11-x+1.1x-12   dydx =…

Q: Find the work done by the force F = xyi + (y-x)j over the straight line from (0,0) to (1, - 3). The…

A:

Q: If F(x,y) is a differentiable function and the equation F(x, y) = 0 defines (y) as a function of…

A:

Q: Find Duf at P f(x,y,z)=4x^3y^3z^3;  P(1,−2,1);  u=1/3i+2/3j−

A:

Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: 2. (a) {(x, y) | y = Vx + 1} (b) {(x, y) | y = Vx² - 1} (c) {(x, y) | y = VI – x} (d) {(x, y) | x² +…

A: If a line parallel to y-axis cuts the graph of the function at most once, then it is a function…

Q: 26 + 4z4 – 2z2 +1 dz (z – 2i)6

A:

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

A:

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: 2. 2sin(хy) at x D 2, у3D Зя/4 3. z= In(x + 1) + y° at the point (0,3,9)

A:

Q: س/ أختار قيمة R ,D المناسبة ل لداله الاتية f(x) = 2 + Vx? - 1 Df = {x:xeR:x 0} O الخيار رقم 1 D, =…

A: The given function is fx=2+x2-1. Calculate the domain and range. Range is defined the all possible…

Q: ux v of u = 2i + 3j, v = -i + j is *

A:

Q: 2- SSi dA A A-{(,3):x7, ソプ andy=x, xy=6,火=8 14.4)' %3D Ans (448) Az ーに

A:

Q: f(x, y) = e&z– 4y af af ду

A:

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: f (x, y, 2) = x³ /+42³y² – xyz +x² – Vz5 VI+ 42°y? – ryz+ x² – Vz5 - -

A:

Q: Let f (z) =iz - 7x. Which of the following is correct ? oi4 = - 7 v, и 3D — olu =7 v oi4 = - 7 v,…

A:

Q: 27. x sec'y dA, R= {(x, y) | 0 < x < 2, 0 < y < T/4} R 28. (y + xy-) dA, R = {(x, y) | 0 < x < 2, 1…

A: For the double integral, ∫ab∫cdf(x, y) dxdy, the limits of integration corresponding to the…

Q: z = f(x, y) = r* – x²y+ 4y, r= g1(u, v) = u² + v², y = 92(u, v) = = uv.

A: Let's find.

Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2и + 3v (b) |u| (c) u-v…

A: Given vectors - u = i+j-2kv = 3i-2j+kw = j-5kPart (a) - 2u+3v = 2i+j-2k+33i-2j+k2u+3v =…

Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

A:

Q: 2. f(x, y, z) = exyz² Find fxyz

A: