Given : y= cos (1-t) and x V2t-t2 Evaluate y' when t=0 O A. y' = - 1 O B. y = 2 Ocy = 1/2 O D.y = 1 A Moving to another question will save this response

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Q: x" +4x'+ 3x = 30 cos(3t), x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put x(0.25)…

A: First we will find the general solution of the given initial value problem

Q: 1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) nt = 23,…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, y(1.3) = y(A)…

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Q: 1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) = 23, 000…

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Q: 1. Given the DE as x(1 – siny)dy = (cosx – cosy – y)dx a) Prove if the given DE is exact or…

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Q: 1. Şuppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: nt B(t) =…

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Q: 10) Find the linear approximation to g(y) = Cos(y+1) at y = 0. Use the linear approximation to…

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Q: The acceleration ā of a particle at any time t is given by à = e-2 î + 3t ĵ+cos t k , then the…

A: The acceleration of a particle is given by a→=e-2t i^ + 3t j^ +cost k^  v(t) = ∫a(t) dt = ∫(e-2t i^…

Q: Given (1+ 3x sin y) dx – x² cos y dy = 0 with y(1) = 0. Using Euler method with h=0.05, y(1.15) =…

A: Euler's method uses the formula: y1=y0+hf(x0,y0) to perform the iterations.

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Q: 2 Consider solving dx using a suitable trigonometric substitution. After performing substitution…

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A: Simpson's rule error bound    Es≤kb-a5180n4 , where f4(x)≤k where ∣E​S​​∣  this e absolute values of…

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Q: 41. * + 4x + 5x = 8 sin t ; when t = 0, x = 0, x = 0. Note that i = is a common notation when the…

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Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

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Q: .1 Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

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Q: x" +4x'+ 3x = 30 cos(3t), x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put x(0.25)…

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Q: 2л 4) Find | cos 0 d0 using Beta function.

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Q: A particle moves along the x-axis with velocity given by v(t) = 8 cos (4t) for time t > 0. If the…

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Q: - Suppose that for a certain leat-cutter ant colony, the birth rate is modelled by: B(t) = 23,000 –…

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Q: A particle moves along the x-axis with position given by x(t) -20 cos (t) – 5 for time t > 0. Find…

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Q: x" + 4x'+ 3x = 30 cos(3t), x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put…

A: Given: x'' + 4x' + 3x = 30cos(3t), x(0) = 1, x'(0) = 2.

Q: 1. (a) Find sin 6x+ cos 4x dx. (b) Evaluate dx. Hence, solve dx. (e' +2) (e'+2)

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Q: 1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t): at 23,…

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Q: 9. Give an equation for a transformed sine function with an amplitude of 3, a period of I1/4, and a…

A: The standard equation of the sine function: y=A sin (B(t+C)) Where A is the amplitude Period=2πB C…

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Q: 1/10 1.A) e* cos(5x) dx integration by parts

A: Here we have to do integration by parts:   Apply integration by parts u as e3x and v = cos5x