Q: Show that the signal x(t) = sin(@ t) is a periodic signal.

Q: b. Periodic Signal whose period is defined by g(t) = {1; 0 ≤t≤1 1≤t≤2-

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Q: Find 7'(t), given ř(t) = ( – 4cos( – 5t), 3 sin( – 5t), e*). - - F (t) =

A: Solve the following

Q: 8. If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dtat t = 0?

A: Chain Rule d(f(g(x))dx   =   f'(g(x)) . g'(x) We have given r = sin(f(t))        f(0) =  π3  ,…

Q: Find the length L of the curve R(t) = -2 cos(5t) /+2 sin(5t) /+ tk over the interval [3, 6]. L =

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Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: Find dt 1- t2 sin (t)

A: Solve the integration

Q: Find the steady-state current in the RLC-circuit in Fig. 71 when R = E = 200 sin 4t V. 50 N, L = 30…

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Q: Eliminate the arbitrary constant/s: y = C1e^ax cosbx + C2e^ax sinbx where a and b are parameters (…

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Q: -을 x e [T, 3 J Sinx =

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Q: Consider the forced linear harmonic oscillator y" + w?y = cos wt where the frequency W = 4 Find a…

A: We are given that y''+ω2y=cosωtwhich can be written as (D2+ω2)y=cosωt.We have to find particular…

Q: Transform F(s) (giving you cos 5t + t³

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Q: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

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Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: 2 sin(t) s(t) = et

A: Part (a) The displacement of the object is, s(t)=2sintet Integrate the expression with respect to t…

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

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Q: (b) Let x1(t) = cos (6tt) and x2(t) = sin(30nt). Determine whether the signal y(t) = x1(t) + x2(t)…

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Q: and as Use the chain rule to find sin(6) r = st, 0 = s + t3 dz as

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Q: (t – sin t)v1 – cos t dt

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Q: Differentiate P(t) = cos(t) ÷1-sin(t)

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Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: consider the analog signal x(t) shown below. The Nyquist rate is X(t)=3cos(507t)+sin(200 at) O 200…

A: Nyquist rate

Q: Find the exact lanth of the 4=1n (sec(x)), Odyct3

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Q: Q2):- Find Y[Z] of signal Geometrical and Nu Y[n] (Cos wn). U[n]

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Q: The function z = r' y is defined on the astroid r = cos 0, y = sin 0 where 0 < 0 < 2ñ. Use the dz…

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Q: derive 8t sin t (d) s %3D cos t t5

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: Evaluates t cos(2t*) dt

A: here we will put 2t4 = u then solve further

Q: Use Part 1 of the Fundamental Theorem to simplify the following expressions.

A: According to fundamental theorem, to find the derivative of the integral, one need to plug the upper…

Q: Plot the following signals in the time range 0sts 30 sec, and determine if these signals are…

A: Solution a: Given x[n]=sin10n Comparing with sinωn So we have ω=10 Since we know ω=2πf⇒10=2πf⇒f=5π…

Q: Find the average power of the signal: x(t) : = cos x + sin x (-7/4, 0) (7n/4, 0)

A: From the given graph, it is observed that the period of function is T0=7π4--π4=2π. Compute the…

Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: Use an appropriate local linear approximation to estimate the value of cos(29°). cos(29°) -

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Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: Assume cos(t) = - where <t <a. Compute the following %3D cos(-t) = sin(t) = sin(-t) =U sin(-t) +…

A: topic - trigonometric ratios sin(-x)=-sin(x) cos(-x)=cos(x) sin2(x)+cox2(x)=1

Q: Consider the forced linear harmonic oscillator y" + w?y = cos wt = COS where the frequency W = 3…

A: The given Differential equation is  y''+ω2y=cosωtwhich can be written as (D2+ω2)y=cosωtGiven that…

Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

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Q: Q6. (A) Compute S[sec² (÷) – 1] sec*)dx. (В) Use Trigonometric substitution method to evaluate…

A: We will find the integrations as following.

Q: find the desivative d the findian bng = sin and compute gh2

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Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

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Q: Use an appropriate local linear approximation to estimate the value of cos(59°). cos(59°) ~

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Q: Obtain the der a) cos(xy)=2y, find y'

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Q: Find the possible values of a and b in the expression u(x, t) = cos (at) sin (bx) such that it…

A: To Find: All those values of a and b such that u(x,t)=cos (at) sin (bx) satisfies the wave equation.

Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: 5. Find Sp√x² + y² dr, where ř(t) = t cos t tsint Ost), 0 ≤t≤ 2π.

A: Given r→(t)=tcosttsint,0≤t≤2π. The objective is to find ∫Px2+y2dr.