Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (6 e 7)i+ (6 e sin t)j+ (6e' cos t) k, t=0 ..... a(0) = (Type exact answers, using radicals as needed.) T+

Q: The first two terms of a Fourier series of a general periodic function are F (t) 2 ; + [3 cos t + 4…

A: Given that, The first two terms of a Fourier series of a general periodic function are…

Q: Solve the given differential euation: + rtan 0 = 6cos0 r = (60 + C') cot0 )r= (60+C) sin® r = (60 +…

A: Explanation of the answer is as follows

Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

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A: Given differential equation: x( 1- siny) dy=( cos x-cosy-y) dx

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Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: Solve for x, if 0 <x S2n, Write your answers in exact values only. sin x +2sin x cos x 0 3 Tt TC 2 2…

A: simplify the equation and find the value of x

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A: Here we have to find the exact solutions of the equation cos(2x)= 1- 3sinx .

Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

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Q: Write a in the form a = a-T+a,N at the given value of t without finding Tand N. r(t) = (3e'cos t)i+…

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Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

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Q: Write a in the form a = a-T+aNN at the given value of t without finding T and N. 3 (5 e'V5)i+…

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Q: 17. Consider the DE y"+by'+cy = 0. If y₁ is a solution of the equation, what conditions must be…

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Q: ý(t) + 100 y(t) = 15 cos 5t + 20 sin 5t, y(0) = 25, ý(t)= 0 V138388 [ y(t) = - Q1 = 2n – tan cos…

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Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (3e' cos t)…

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Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

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Q: (1 + cos 7t) 2 sin 7t dt

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Q: f (x) = cos(3r)[2 + sin(3r)]* on 0, O e*(16) - e*(7) O e*(-16) - e*(7) ) 1.52x10*(-4) O In100 - 9 O…

A: ∫avg=1b-a∫ab(cos3x)(2+sin(3x))4  ∫avg= 1π6-0∫0π/6cos3x2+sin(3x)4 dx        ....(1) Now to calculate…

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A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

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Q: 1. Consider 3x + sin x – e* = 0, using Secant Method with initial points xo = 0 and x1 = 1,…

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Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

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Q: The differential operator D2- 8D+80 has the form D2- 2aD +a² + B? where a = and B= Therefore D - 8D…

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Q: dr Solve the given differential euation: + rtan 0 = 7cos0. de %3D r = (70 + C') cot0 Or = (70 + C)…

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Q: Show that y(x) = cos-(Acot x) + B is the general solution to the Euler-Lagrange equation for the…

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Q: Find the smallest value of t such that t>0 and sin(8t)– sin(3t) =0.

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Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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Q: Q1\ Prove the left side equal to right side in the following : * L-1 (s² + a²y² - [sin at + at cos…

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Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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Q: 1. Solve the hyperbolic function of the following. i Prove that coshx – coshy = 2sinh (*) sinh ().…

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