Find f(t). 2s + 3 s2 + 4s + 13,

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: F(s) = (8s + 11)/[(s-4)(s²+9)] %3D

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: f(t) = te3t cosh 4t s²-6s+7 s2-6s-7 А. (s2-6s+25)2 С. C. (s2-6s-25)2 s2-6s+25 В. (s2-6s-7)2 s2…

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Q: Determine L-1{F(s)} 2s+1 sF(s) + 3F(s) s2+2s+1

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Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: 3 11. f(x) = Vx-6Vx 12. f(t) = t3 -t3 +4 ww-

A: Basic derivative formula can be used to solve the questions. ddx(xn)=nxn-1ddx(cosx)=-sinx

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Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

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Q: f(t)=t²(3-2t)³ at t=1

A: Given function: ft=t23-2t3 Find the value of given function at t=1

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Q: - r)rdrde 32(V2-1) 16(VZ-1) c. VZ-1) 4(VE-1), S(V2-1) a. d. 3. 3 3 e. 3.

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Q: D={(x,y):4 < x² +y² < 81,< x <-V3y}, V3 Find [S, dA JJp y2

A: We will use polar co ordinates to solve the problem

Q: 2s (s² + 1)² 3) Find L¹ 40 by using the convolution theorem.

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Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

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Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

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Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

Q: x3y5 Q3: Let x = 2 ± 0.005 ,y = 10 ± 0.01,z = 20 + 0.01 find u = %3D And fined the error ?

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Q: Q.2 a- If w=xy+ find y2 +1 a²w a²w and дхду дудх

A: Solution Part A  Given. w = xy+eyy2+1  We have to find ∂2w∂x∂y   and  ∂2w∂y∂x

Q: d²y x-9 Find for y dx2 = (3x² –2x+5)

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Q: 2t + 7 f(t) = t- 3 %3D h(n) = - 2n2-3n+1 %3D f(h(-1)) =

A: Here we have two functions f(t) and h(n), we want to find the value of f(h(—1)). To find f(h(—1)),…

Q: Q4: Find and classify the extreme points of f (x, y) = 3x?y+y3 - 3x2 – 3y2 +2.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: (s-2) F(s) = [+ %3D (s-2)2 + 16

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Q: Find f(t). f(t) = 6e9r { 14 +54 +e⁹t 6s (s - 9)²) X

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Q: 2a V2ax 2ах f (x, у) dydx (a > 0) е. 2ах-х2

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Q: Find F(s). {16e + 1) Wce - 13} (6t + 1) U(t F(s) =

A: We have to find Laplace transform of given function using Heaviside Shift Theorem.

Q: S2-3x', x>2 Vx -2, х <2 а) g(x)-

A: The given function is gx=2-3x3,   x&gt;2x-2,    x≤2. Sketch the graph of this function as shown…

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

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Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: f(t) = te3t cosh 4t s2-6s-7 А. (s2-6s+25)2 s2-6s+7 С. (s2-6s-25)2 s2-6s+25 3. (s2-6s-7)2 s2-6s-25 D.…

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Q: y = v1 - x2 from a = 0 to r = ;

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Q: find df $(x.g) = Xy+y²-3% X = t- 3t y = 5t3

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Q: is the minimnurm step of the horno gone ous n What X+ xt 2-X ifferential equatian with its solution…

A: The objective is to find y=x2e-x+x3+x2what is the minimum step of the homogenous differential…

Q: dy Given y= x³In x, -is dx A 3x2In x B B 3x2in x+ x2 ( c) x2 D 3x2

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Q: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

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Q: d²y Find for y dx2 x-9 (Зx2-2х+5)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3x The y, of y''-6y'+9y = by using variation of parameters is: .A Y,(x) = -In(x). e 3x 3x -e |

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Q: 2s -5t f(s,t) = %3D 4s +t %3D f =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: d²y Find if x = t – t2 and y =t – t3 dx2

A: Given:

Q: Q5/ Find by using chain rule dx y = vt - 5 +t, x = tV4t + 8 +7 %3!

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Q: 4. f(t) = V3 – 2t , find f""(t) %3D

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Q: + Vs + es +- ds n = 3 From left endpoint s² + 1

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Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: E R D. -2x - 6 M - N NL = K 2x - 14 SR = x+ 15 x+2 wV = |x+21 FD WN =

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Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-