The eigenfunctions for the BVP: 00 2 u(0, t)=0 u(1, t)=0, are X,(x)=sin(nTtx); n=1, 2,.. Then f,) = %3D O a. f,1)=2t 22 (-1y*1 b. с. 2t(-1)" d. t(-1)"+1

Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: a2f дхду' a2f 2. (a) If f (x, y) = x tany + ye-2*, find and What do you notice? дхду (b) If f(x, y)…

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Which of the following is not true for the differential operators A, B, and C? A (A+B) +C = A+ (B+C)…

A: Differential operator

Q: In (*-") l+V1-x2

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Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: Determine exact solutions for the equation 2sin'x – 3sinx +1 = 0 in the interval xI [a, 3n].

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Q: All Sections 1) Solve the following equations for t Jy evt = 2) Find the derivative of y with…

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Q: y'" — 7y' — бу = 0

A: Solution :- This higher order differential equation can be solved simply by using complementary…

Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

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Q: (4) M" - afg' -4fg= 0; Y@-1, g'()=0

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Q: se-2s -)=D 's²+45+3

A: Given,

Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

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: Find the exact lanth of the 4=1n (sec(x)), Odyct3

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Q: Determine coefficients a and b such that p(x)=x^2+ax+b satisfies p(1)=6 and p′(1)=0

A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: Compute r"(t) and r'''(t) for the following function. r(t) = (7t2 + 4,t + 3,6)

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Q: Calculate zu for z = 2x-y 1, x = e²u cos(3v), y = e²usin(3v) x+3y'

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Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

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Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: Solve the system [: 16 -36 dx dt 6. -14 with the initial value 13 x(0) 5 -5e^(4t)+13e^(-3t) x(t) =…

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Q: Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

Q: What is dy/dt of the given? Show both the simplified and unsumplified answer.

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Q: 1.16. (a) If f and g are differentiable scalar functions, show that V(fg)=fVg+gVf.

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Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: Letr' (t) = (3 + 4t, cos(t), 6e³t) and 7(0) = (7, 2, 5). Determine r* (t). r(t) = ([ (..)

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Q: Find f'(z) when f(z) = J, 0, if z = 0 if z = 0

A: fz=z¯ 2zif z≠00if z=0 To Find: f'z