L(sin Vf) = V. 2s

Q: Find the sine transform of 1 and deduce that et - eT TLX F, (cosech Tx)= 1 tanh (p/2).

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Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: Find the integral of ∫tan^5(4x)dx

A: Given Data: Integrand: ∫tan54xdx   let u=4x   The derivative of the above equation is, dudx=41dx=du4

Q: A damping system with a negligibly small spring constant is modelled by x"+bx'=aebt with x(0)=0 and…

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Q: The integration expression Jsin(3In(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable…

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Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

Q: Find the differential of z = sin²(5x) + ev

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Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

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Q: 글 sin (26) + 좋cos (3t) CoS

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Q: 5. Given that L{ sin VE} = 1/2s T /se-/4. determine the Laplace transform of (1/Vecos vt. %3D

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Q: Q5. Find the Laplace Transform of the funcetions x(t) and yit), which satisfy the coupled first…

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Q: Find Fourier sine transform of - and deduce that

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Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

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Q: Integrate (three) of th 1) f sin6x cos3x dx

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: 5. Use differentials to approximate V4 + In(1.2) correct to two (2) decimal places.

A: Let us take the function f(x)= √x f'(x)=1/(2√x) f(x+Δx)=f(x) + f'(x) . Δx   ___i) Here let us…

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: 2 If the functions y = sin x and y = cosx are both subjected to a horizontal compression by what 3'…

A: Given: The function y=sin x and y=cos x are both subjected to a horizontal compression by 23

Q: Compute the Laplace transform of integrate t to 0 te ^2t sin 2t dt

A: Given  : f(t) = t e2t sin2t To Find : laplace transformation Lt e2t sin2t

Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

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Q: Find the Laplace transform of tant. Show your full Solution.

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Q: What is the value of the inverse Laplace transform given by L 2s+1 8 J s2 +2s +3 O a. e-t (2…

A: Some Laplace inverse transform formulas: L-1(s-a)(s-a)2+b2=eatcosbtL-1b(s-a)2+b2=eatsinbt

Q: Find Fourier transfarm f x #1= cos aut ut

A: Given the x(t)

Q: Use a linear approximation (or differentials) to estimate the given number.   27.tan 2°

A: The Linear approximation of the function at x=a is given by L(x)=f(a)+f'(a)(x-a) To Find Linear…

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: y' = 8x x(0) = 1 %3D x' = 2y y(0) = 0 %3D

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Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

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Q: Use Laplace Transforms to solve the initial value problem. x"+x = sin2t; x(0)=0=x'(0)

A: Solution of Intial value problem using Laplace transferom

Q: •t Set sin 2t dt

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Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: Use differentials to estimate sin (π/6 + 0.01).

A: Use differentials to approximate the value of sinπ6+0.01 The nearest number to sinπ6+0.01 whose sine…

Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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Q: This is exercise 26 of Section 7.5 page 460. Find the integral æ* sin(æ²) dx-

A: Answer is given in the picture

Q: Prove the following continuous time Fourier transform relationship. sin(at) 1 X(N) = Continuous Time…

A: Fourier inverse of XΩ=1    -π≤Ω≤π0    otherwise is : F-1XΩ=12π∫-∞∞XΩejΩtdΩ…

Q: Show complete and orderly solutions. Simplify all final answers whenever possible. Using…

A: L(Cosh at).

Q: Find the sine transform of and deduce that TUX e 1 tanh (p/2). |(2x) F, (cosech rx) = %3D

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Q: 4s – 9 - F(S) %3D 4s² – 16s + 9

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Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: Compute for a real root of 1 2 cos Vx – sin vx = accurate to 4 | 4 significant figures using…

A: 2cos(33)-sinx=14;   x0=π f(x)=2cos(33)-sinx-14 f(x)=0 ⇒2cos(33)-sinx-14=0 x=cos-11214+sinx3=ϕ(x);…

Q: Differentiate the following functions 4 1-cos2x Y = by chain rule. 1+cos2x

A: To differentiate the given function.

Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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Q: Explain in your words how the Laplace transform is applied to solve a system of linear deferential…

A: The Laplace transform is an integral transform. The Laplace transform is mostly useful in solving…