C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

Q: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; x y = t, z = t8 t'…

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Q: Use Euler's method with h = 0.25 to compute approximate value of y(1) for the IVP: (a) dy 1 = y sin…

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Q: dw 12. Let w = xey/z. Find the value of -at x = t?, y = 1-t z=1+ 2t dt

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Q: w = xy, x = e", Given Find dw/dt

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Q: The solution of D.E y" -y = 5(t – 1) ,y(0) = 0,y'(0) = 0 Select one: O a. Uq(t)cosh(t – 1) O b.…

A: To solve the below differential equation.

Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (d) z = sin (4x + 5y); x = s + t, y = s - t

A: Given that, z=sin4x+5y ; x=s+t ; y=s-t Then we get, z=sin4s+t+5s-t⇒z=sin4s+4t+5s-5t⇒z=sin9s-t

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 9 cos xy – sin xz; x = y = t, z = t3…

A: We have to find

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Given dy dy dz² +2 + 5y = e dr and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the…

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 4 cos ry – sin cz; x=÷, y = t, z= t8…

A: Given,           w = 4 cos zy - sinxz;            x = 1/t ,      y=t,        z= t⁸

Q: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; 1 x = ; y = t, z = t8…

A: A detailed solution is given below

Q: Given z = 2 cos t + 33 and y = 8 sin²t dz (i) dt dy (ii) dt dy (iii) dr

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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: dw 3) Find dt if w 5 cos(xy) – sin(xy), x =,y = t, z = t3 at at 4) Let t =,u = x² - y? ,v = 4xy³.…

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Q: Given z = 17 In(t) and y = 289 t then fir dy d'y dx?

A: Differentiate given function

Q: Given z = 14 In(t) and y= 196 t then find dy %3D dx dy ||

A: Given a parametric equation:                                    x = f(t) , y = g(t)  the first…

Q: Given dy dy +2- dx + 5y = e and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the %3D…

A: Hi! You have posted multiple questions. As per norms, we will be solving only one question. We will…

Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: D. z= X = Cos t, y = sin t; t = T/2 y? + 1'

A: Given query is to find derivative of the expression.

Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: Use the Chain Rule to find dz/dt. z - x2 + y2 + xy, x = sin(t), y - 2e Use the Chain Rule to find…

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Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: 3y" (t) – / (t) = e' cos(t) + sin(t), y(0) = 0, y'(0) = 0 -

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Q: The general solution dx/dt t+x of t > where t > 0, is x(t) =

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Q: Let y, = sin(t) be a solution to t y" -y' +4 t y=0. If y(t) is the solution to the I.V.P ty" -y' +4…

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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: dW w. if W=3x3+2y³ ; where x= e, y= cos 2t at t=0 dt Find

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Q: at (s, t) = (0, 1) if ds z = 6x + y² tan (), x = e" – st, y = s² – f.

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Q: Find dw/dt at t=0 for the function w=sin(x),cos(y),ln(z). Where x=-7t^2+9t+pi/2, y=t,z=e^-6t

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Q: a) Find the differential dy. y = ex⁄2 dy = ? (b) Evaluate dy for the given values of x and dx.…

A: Explanation of the answer is as follows

Q: dx/dt = t+x t> 0, The general solution of x(t) = where is %3D

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Q: 1.Evaluate S. (x² + y² + x²)-²ds where C is the helix x = cost, y = sint, z = 1 for 0 < t ST

A: The length dS is: ds=dtdxdt2+dydt2+dzdt2=dt-sint2+cost2+02=dt

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; x = ;, 1 y = 9t Enter…

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Q: Evaluate dW at t = dt for the function W = xy x = sin t, y = cos t, z = t². 4 49л2 972 9x2 4 49л

A: Given: W=xyz,x=sin⁡t,y=cos⁡t,z=t2 Substitute the value of x, y and z in w , we get W=sintcostt2…

Q: dz Use an appropriate form of the chain rule to find dt z = 4x°y³; x = tº, y = t" Enter the answer…

A: From the given problem: z=4x6y3 ; x=t8 , y=t7 Now apply the chain rule.…

Q: Find dw/dt at t 1 if w xe + ysinz - cosz, r ! = 2/t, y = t – 1 and z = nt.

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Q: Given z = 2 cos t +35 and y = 8 sin t %3D %3D dx (i) dt -2*sin(t) %3D dy (ii) 16*sin(t)*cos(t) %3D…

A: Given x=2cost+35 and y=8sin2t

Q: Use the Chain Rule to find dw/dt. x = 6 sin(t), y = 2 cos(t), z = 9 tan(t)

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = y = t, z = t³ t…

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: • 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) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: dz Use an appropriate form of the chain rule to find dt z = 3 cos sin ry; y = 7t Enter the answer in…

A: Here, the given functions are: z=3cos x-sin xy; x=1t, y=7t

Q: Use the Chain Rule to find dw/dt. w = In( V x2 + y² + z? ), x = 2 sin(t), y = 7 cos(t), z = 8 tan(t)

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Q: Find the particular antiderivative that satisfies the following conditions: dx = 5e' – 8; x(0) = 2.…

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Q: dz Given z = e* sin y,x = u² + v²,y = uv, find dv

A: Using chain rule of derivative,

Q: 6. Let r = t sin t, y = t cos t, 0<t<1. dy (a) Find dr

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