c fx) = at (4, 2) 3x – 4 d y=x In x at (0, 1) sin3x at y =- x? 4 e T 2

Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: dz az C. Find ax and 4. 5x*y?z-y cos xz = 2x°+y

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Q: fx) = Зх - 4 at (4, 2) d y=x In x at (0, 1) sin3x y = 4 at T 2

A:

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: tan 0 d 30. dO sec² y dy

A:

Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

A:

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: I need help to find particula solution using undetermined coefficients: y''+4y = sin(t) + t2 + et

A:

Q: T T 68. y = sin 3 + 4 %3D -

A: Given data:     The given expression of the function is: y=sin(-πx/3 – π/2)+4.     (a) The general…

Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: 2m (b) S* dz. VI+3 sin z cosz

A: Explained below

Q: Q.1B) Show: 2x 1 √ π.χ. sin- dydx + 2y SS || 2 √√ 4 (TT-+-+2²) π.χ. sin dydx = 4 2y

A: We have to compute the double integral. It is difficult to evaluate the integral. So we will change…

Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: find dy>dt.                                                        y = cos4 (sec2 3t)

A:

Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

A: The given equation is: x2sin(2y-5z)=1+ycos(6zx) To find ∂z∂y, differentiate above equation w.r.t. y…

Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: Q1: If Z = x³ + y* + (x sin y) + (y cos x), Find Zx/Zy?

A: We are given: Z=x3+y4+(x sin y)+(y cos x)To find: ZxZy This can be calculated as follows:

Q: - (2y cosx + sin* x)dx : sin x dy, when x =y= 1 %3D

A:

Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

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Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

A:

Q: SV1- x2 sin-1x dx

A:

Q: Find the area between the two curves.

A: The area between the curves y=sec2x and y=sin2x on interval 0, π4:The area between curves is the…

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: B. Substitution as suggested by the equation 3. (x + 2y – 1)dx + 3(x+ 2y)dy = 0 when y(0) 4.…

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i и

A:

Q: (d) (.9.z) = arctan(y/F) + sin (3 + ry-5y).

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: 2X Qul If y = Fird dy e %3D (x? +1) (I+ sinx)

A: We use logarithmic differentiation

Q: Find y' at the point (4, 4) where z sin(z² – y²) + 13 = 2² – 3.

A:

Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

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Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: Solve the DE when all conditions set to zero. (D² + 4)y = sin²2x

A:

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

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Q: dy Given that y =÷-sin3x . Find de 2 18. 4 +3cos 3x A B 4 -3 cos 3x 4 3 cos 3x C +3 cos 3x O A Ов

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Q: Obtain the solution (3tan x-2cos y) sec^2x dx + tan x sin y dy = 0

A:

Q: Obtain the der a) cos(xy)=2y, find y'

A:

Q: a) Prave that sinlx t Cos-lx = ½ %3D

A: To prove,   sin-1x+cos-1x=π2

Q: What is / 2sec²y dy? S 2sec?y dy = 2 sin (y) + C S 2sec²y dy = -2 tan (y) + C S 2sec²y dy = – tan…

A: Please see the answer below.

Q: Evaluate the followingintegrals.

A: ∫0π6sin 2ysin2y+2dyFormulasin 2x =2 sin x cos x integral formula∫dxx=lnx+C

Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

A: Partial derivative of a function of two or more variables with respect to one variable is the…

Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

A:

Q: Solve the fo llowing D.- E y + y tan X Cos X %3D

A: