4) Find ôw/ ôr if w= x=r-s, y= cos(r + s), z = sin(r + s) at the point (r,s)= (1,–1) Ans. 12

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A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

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A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

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Q: 10. sec (10t) tan" (10t) dt 11. tan" (2w) sec" (2w) dw / cot (3r) csc® (32) dæ 12.

A: As per our guidelines, I can answer maximum one question. Since you have asked for three, So i did…

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Q: sin r 4. Compute J r(I) dr.

A: Evaluating the given integral.

Q: What is the value of t in terms r, s, and u In the equation

A: The solution is easy to see

Q: Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given…

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Q: O y(1) = c, e*" + C,e For each set of solutions below, match the solutions to the general s Prompts…

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Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: z = sin(6x) sin(5y) az az dy II

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Q: Compule he an Curvc given aM byO x= and ye 3tcos(t) 'from DLtL engh ot M pacbmeter 3t Sin (t)

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Q: Find dy Y= #an" (=) + cos "(sx) + CoS

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Q: Find all complementary functions of the equation y" - 4y' + 4y = 0. a. cos2x, sin2x b. e-2x,xe-2x C.…

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Q: If x'y" +xy' + (x2 - -0 x>0 , V1=X 2 sinx and y=y,v. Which of the following equations satisfied by v…

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Q: If x²y" + xy' + (x² – ÷)y=o x >0 ,V,=x 2 sinx , and y =y;v. Which of the following equations…

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Q: I need the answer as soon as possible

A: As we know that, eiz=cosz+isinz                   ...(1)And,e-iz=cosz-isinz                ....(2)…

Q: (c) y/" + 4y = 3r cos(2r)

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Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: Yp = A1 cos V2t + A2 sin V 2t Which of the following is Yp'? sin v2t A1 V2 Cos /2t A2 V2 O V2A1 sin…

A: Please see the explanation below

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: If x³y" + xy' +(x? -y=D0 x>0 ,y,=x sinx , and y3V,v. Which of the following 3 equations satisfied by…

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Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

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Q: ry"+xy'+(x* -y =0 -)y = y = x cosx is a solution of the equation Show that

A: Given               x2y''+xy'+(x2-14)y=0                      (1)

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A: Topic- differential equations

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: daffəx and åf/ðy y) = x² – xy + y² v) = sin? (x – 3y)

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Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

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Q: i. y" - 4y + 5y = 39xe* sin(x) + 47e * sin(x)

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Q: 2. y" +4y= sin2x + x2 using inverse operator method

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Q: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…