For 2 consider s(t) =r -9 +24t on [0,6] Find v(t)and a(t). At what time does the particle change direction? For what values of t is the particle speeding up?

Q: dz Use an appropriate form of the chain rule to find dt z = 9x10y%; x = t10, y = t6 Enter the answer…

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Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: Find the general solution to y"(t) = t1² – 3t* + e' – nsin (at). Show all steps

A: y"(t)=t12-3t4+et-πsin(πt)d2ytdt2=t12-3t4+et-πsin(πt)

Q: dw Use an appropriate form of the chain rule to find dt = In(10x² – 2y + l2³); x = tỉ, y = tỉ, z =t?…

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Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: dx Q2 / Use the chain rule to find ( ) in terms of x and y dy y = ( 2 1 1, at t2 t = 2 and X t + 1.

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Q: The position of a particle moving along the x - axis at time t is given by x(t) = e©os2t, 0stsn. For…

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Q: The position of the particle at timet is given by s(t) = t² – 16t + 63. - The particle is moving…

A: Given data: The position of particle is given by, st=t2-16t+63

Q: The position of the particle at time t is given by s(t) = t² – 12t + 35. - The particle is moving…

A: Velocity and position

Q: Q4. If y= f (t) and x=f (t) d²y dx2 dy 3 and %D 4t dx2 dy By using chain rule, find dt

A: Chain rule is given by dy/dx=( dy/dt )× (dt/dx)

Q: Let y = 2x². Find the change in y, Ay when I = 4 and Ar 0.1 Sesse Find the differential dy when = 4…

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: a) Find the general solution for UTM dy TM dy +2- dr? dr (1+f) UTM (77 +1)xz² = fip +

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Q: Find r(t) that satisfies the initial condition(s).…

A: Given: r(0)=2i

Q: Use Euler’s method with n = 2 on the interval 2 ≤ t ≤ 3 to approximate the solution f(t) to y′ = t -…

A: Given, y'=t-2y y(2)=3

Q: Find dt(t=1.s=0) dz when z 2x3 + 15y, where x t? -s and y =t+ 2s? %3D Enter the answer in the space…

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Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

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Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: dz Use an appropriate form of the chain rule to find dt z = 6x°y3; x = t8, y = t 52,3. %3D Enter the…

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Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: Q3. Use fourth order Runge-Kutta with h = 1/4 to compute approximate values of y(1). y'= y(1 + e 2*…

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Q: 4y"-y=e^x/2+6 consider the following DE to be solved by variation of parameters

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Q: sing the method of variation of parameters to e a nonhomogeneous DE with = -ex, W2 = e W2 = e-1Ix…

A: Wronskian of the function

Q: Approximate V 34 using differentials. A 2.023400 B 2.024397 c) 2.025000 D 1.975000

A: Given (34)^(1/5)

Q: dw given w = a2 + 2y2 + 22 and a = cos (st), y = -2s Int and Use chain rule to find 2 = 3s' Vi.

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Q: Find the differential of the function. u = 2x3 + 7 du = | 0 %3D

A: Given, To find Differential of u=2x3+7

Q: dz Use an appropriate form of the chain rule to find dt z = 2a°y®; x = t³, y= t10 Enter the answer…

A: Explanation of the answer is as follows

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: solve for y in terms of t or x, as appropriate.

A: given: lny=-t+5 we have to solve for y in terms of t or x, as appropriate

Q: Find ∫C (ez - 1) / z  dz with C being z(t) = eit for 0 ≤ t ≤ 2π

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Q: c) Show that y(x) = 1+ax+bx², where a and b are non-zero, is a solution to Laguerre's equation, d²y…

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Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

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Q: For f(æ) = e? + 0.39a? – 2 with æo - 4.9 and æ1 1.9 apply steps of the secant method to obtain 22 =…

A: The root of the function can be calculated using the secant method. The formula for the secant…

Q: Let y = /7– 2. Find the differential dy when a = 4 and dæ = 0.4 Find the differential dy when æ = 4…

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Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

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Q: Ql: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: For y=f(x)=x²-2x+7, find dy and Ay, given x=4 and Ax= -0.2. dy=(Type (Type an integer or a decimal.)

A: Use formula and put value

Q: Q16: Consider the D.E. (x – 1)³x²y" – 2(x – 1)xy' – 3y = 0. Is xo = 0 an ordinary point? Explain…

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Q: dz Use an appropriate form of the chain rule to find dt z = 6x°yl0; x = t³, y = t³ 10. Enter the…

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Q: Q2: Sdve the differential eqpeation d²y =20"t 9Sin 2x -2Cos 2x %3D

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Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

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Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: ) Find the direction in which f (x, y) = x²+xyincreases most rapidly at P(1, –1).

A: 1.) given multivariable function is, fx,y=x2+xy and point is P(1,-1). Divergence: Divergence of the…

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: Q1: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

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