• T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by F(t) = (12 sin(3t), 10…

A: Given: ∫C(x+y+z)ds, where C is parametrized by r→(t)=12sin(3t), 10cos(3t), 211cos(3t) for 0≤t≤π.

Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: b) Find the potential P(x,y) attached to the exact ODE 2r sin(y) + x* cos (y) y = 0

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x – sin ry; y = 9t t %3D SSEVS Enter…

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Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0) %3D

A: Separation of variables.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: y=6 In(cos(e7")). dy AeBt sinC (e7 dt Then %3D cosº (e7) where A = %3D %3D D = BCD

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Q: #2. | Ax)dzx, f(x)= (sin z, 0srs a/2 |cosr, n/2< rSA f(x)dxr. f(x): #3.

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Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: Find x(t) and y(t) by substitution/elimination. dx 9y + 20 cos(t) dt dy dt 10 cos(t) x – -

A: System of linear differential equation:

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

A:

Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m − n)] dx…

A: Let's find.

Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

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Q: dw Use an appropriate form of the chain rule to find dt 1 y = t, z = to w = 3 cos xy – sin xz3; t'…

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: (a) f(x) + cosh(47) (b) f(z) = VI In(|tan(9r)|) tan n(x) psin(z) 12 (c) y = dt

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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Q: Q1:- dz at t=al4 at Calculate z = f(x, y) : 4x² + 3y?, x = x(t) = sin t, y = y(t) = cos t %3D

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: x dx = e* + cos x e* + sin x O a. In(e* +sin x)+C O b. In(e* + cos x)+C О с. - In(e* + cos x) + C…

A: To evaluate  ∫ex + cos xex + sin x dx

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; 1 y = 7t Enter the…

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Q: dy 1- Solve = cos x + y, where y = dx 2.0 at x 0 take step size h = Ax=

A: Given,         dydx=cosx+y Where y=2.0  at x=0   and h=0.1

Q: dv dv 5. Use the Chain Rule to find and ds v = ln (2.x + 3y), where x = s sin t, y =t cos s %3D

A: Here, Givenv=ln(2x+3y)∂v∂x=22x+3y∂v∂y=32x+3yAlso, x=s sin(t)∂x∂s=sin(t)∂x∂t=s cos(t)y=t…

Q: a)  Find the differential dy. y = cos(?x) dy = ?       (b)  Evaluate dy for the given values of x…

A: We have to find the following given conditions according to the given condition

Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

A:

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: A)lf y = sin¯¹ (3) prove Zyy + z = 0 B)Z = 1+ Ini, find [21.

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: r nosへSう'" ( メンン 2 COS(SIn (x))

A: Let, cos(sin-1x)=t⇒sin(sin-1x) 11-x2dx = dt⇒x11-x2dx = dt...(1)

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: S(t) dt = In(x) cos(r) + sin(3) e-² sin(3) "S(t) dt, find f(r). ven

A: The expression is given by ∫sin(3)xftdt = ln(x)cos(x)+∫sin(3)xe-t2ftdt                            To…

Q: 10 cos(x) Evaluate the improper integral: / dx Vsin(x) а) 30 b) O20 40 c) 3 d) Odiverges e) 10

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Q: dv dv If V = ÷f(0) and x = r · cos 0 , y = r · sin 0 . Prove that x -+y÷= -V dr dy

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Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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Q: In the given DE, cos x + In y + ( + ev = 0, integrating the coefficient of dx, M (x, y), with…

A: We will find the g(y) as shown below