If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

Q: Hw X+22=9 zy +7=8 4X -3y =-2 Aus , X=1 ,u=2 ,Z=Y

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Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

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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: y"(t) – 4y'(t) + 5y(t) = e"U (t – 2), %3D

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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: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find (au/ay), at the point (u,v) =(√2,3), if x = u² + v² and y= uv. ди (2) = (Simplify your answer.)…

A: Given: x=u2+v2 , y=uv, and u,v=2,3 Given query is to find indicated partial derivative ∂u∂y2,3 If x…

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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

A: Given x=u2+v2,y=uv   u,v=2,-2

Q: z+2 dz cot (z²+4z-3)

A: To evaluate: I=∫z+2cot(z2+4z-3)dz⇒z=12∫2z+4cot(z2+4z-3)dz...(1)

Q: 8. Let D be the rectangle given by -1<ys0, 1s x< 3. calculate ff,(x2 + y)dydx

A: 8. We will evaluate the given double integral. Given integral is ∬D(x2+y)dy dx with the limits…

Q: 2 W = Span- - 1 1 .Then, the distance and y = 1 -3 -21 3 11 ny to W is

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Q: y''+2y'+2y=r(t), where: r(t)={10sin2t if 0π ; y(0)=1 ; y'(0)=-5

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Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: c. y" – 8y' + 20y = te', y(0) = 0, y'(0) = 0 %3D

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Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: Se-2t if 0 3,

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Q: dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 =…

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Q: Find y' for x^4y^3−3x+2y=24 at the point (−2,1).

A: We have, x4y3−3x+2y=24 Using the chain rule of differentiation,…

Q: If y = (x + 1)(2x – Vx), then y' will be,

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Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

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Q: Calculate and at the points (1,649, 5) and (1,649, –5), where z is defined implicity by the equation…

A: The given function is  z4+z2x2-y-1=0  We have to find tha partial derivative of z w.r.t. x and y at…

Q: D.(1,2), where f(x, y) 14x-y in the directionof v (2,-1)

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Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

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: If A = 2x2'i– yzj +3xz'k and ø=x³yz, find V×(ø4)at the point (1, 0, -1).

A: Given A = 2xz2i - yzj + 3xz3k and  ϕ = x2yzSo, ϕA=  x2yz(2xz2i - yzj + 3xz3k)     =  2x3yz3i…

Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: Find at (2, -2, 1) if dy x2 + y? + 22 = 6xz + 6yz + 21 %3D

A: Given that x2+y2+z2=6xz+6yz+21 Then we have to find ∂z∂y

Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

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Q: 26 + 4z4 – 2z2 +1 dz (z – 2i)6

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Q: e-", if 0 3,

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: Find y' for x^2y^4−3x−3y=13 at the point (−1,2)

A: Given Data: Equation: x2y4-3x-3y=13 Point: x, y=-1, 2   Differentiate the above equation with…

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: Let fa)--1 and g)- -'+x-3 Which equation shows Ma). where M) – W.g A Mz)-x+x+3 8 M3)- -+ -4 C Kx)-…

A: Definition used -        Product of two functions - When we multiply two functions, We will get…

Q: Calculate Duf(0,–2,5) in the direction of v = -3i + 12j – 4k for the function f(x,y,z) = 3x² + xy –…

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Q: If = =x - xy + 3y and (x, y) changes from (3. - 1) to (2.96, - 0.95), compute the values of A: and…

A: Given that            z = x2 - xy + 3y2 and (x,y) changes from (3,-1) to (2.96, -0.95). We have to…

Q: Sove the IVP y" + 2y' + y : if 0 4

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

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Q: T(x,y) = x + xy + y - 12x + 2 on the rectangular plate 0sx<9, -5<ys0

A: We have to find absolute minima and maxima of given function.

Q: F (r, y) = (3x²y² + cos y + ye", 2ar*y - - r sen y + xe*)

A: Given F→x,y=3x2y2+cosy+yexy,2x3y−xsiny+xexy. We have to determine whether the vector is gradient…

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

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

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Q: Determine Df(4, -1,6) for f(x, y,z) = ery +4zx in the direction of (-3,2,6).

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Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

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Q: Solve for fxx, fxy, fyx and fyy given f(x, y) = 2 ln(x − y).

A: The given function is:fx,y=2 lnx-y.We need find fxx, fxy, fyx and fyy

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.