HW 1: Find the trigonometric Fourier of the triangular waveform shown over the interval (-t, t). x(t) 2 - t -2t 2 Answer: x(t) ="E% 1 Z n=1 n2 n odd cOs nt - T

Q: Q3. Fourier Find all frequency components spectrum (amplitude and phase at each frequency) of the…

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Q: Select the corect answer a. (s-3 Ob. (s-3) Oc 1 (s–3)? Od. (s–2)} O e. 1 (s–3)

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Q: 4. Evaluate -2π 1 (a) √² indy. (b) fo 3+sin 1 2+cos y dp. (c) f 1 (2+cos y)2 dp.

A: a. The given integral is: I=∫02π13+sinφdφ               I=2∫0π13+sinφdφ               1 Use…

Q: Which of the following equations are exact?

A: A differential equation of the form  called exact if and only if .

Q: cos(2z) dz c = |Z| = 1 Evaluate where at oriented 5-4 cos(z) counterclockwise?

A: Let fz=cos2z5-4cosz Singularities of f are those points where the denominator is zero. So, put…

Q: etion) 16 sin? (4/7) cos³ (2VI)

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Q: 0Z for the function : a x Find x2 sin ( y ) + x e cos ( z? ) = 3 y - 6 z + 8

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Q: | sin # da, (h) cos 9 sin 0 de. Ans. (u) 16/I5. (b) 8/10. Evaluate (a)

A: (a). In this part, we use reduction formula to find the value of the given integral. (b). In this…

Q: curier series representation of the periodic function below if c = 4.4 and d = 16.3. Then, find the…

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Q: Select the graph that best matches the function. = -4 cos(x + ose y = O a) TL (-1/2, 4) (3x/2, 4)

A: Given equation:- y=-4cos(x+π/6)  To find:- Sketch the graph of given equation

Q: (In3+j5)5 sech(5.5430°) tanh j 4 V[ej – j213 ji]4 Evaluate the function above. Key in your answer in…

A: Given tanhjπ4ej-j213jj4ln3+j55sech(5.5∠30°)

Q: sin-1x If y = dy cos(t) dt, then dx Select one: a. cos(sin-1x) b. X /1-x² c. Non of them d. 1 e. 1…

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Q: Use the triangle to express 8 as a function of y. 10 08 = sin() 0 8 = sin n-¹(10) 0 0 = cos 1¹ (1)…

A: We can find the correct option in the below steps.

Q: f(x) 2. Consider the periodic function given by f(x) = x² over the interval (-x, x). A sketch of the…

A: Given periodic function is fx=x2 over the interval -π,π The average value of the function over the…

Q: f(0) = -2sin(2(0- 45))+1 Centerline: Max y: Amplitude: Min y: Period: Frequency: Phase Shift:…

A: The general form of a sinusoidal function is y=A sinBx+C+D. Here A is the amplitude, C is the phase…

Q: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

Q: L2 cos (0) + L, cos (a - 0) | y = y1+L2 sin (0) – L, sin (a – 0). Combining the above two equation.…

A: for cosα we have to find way to eliminate θ . For tanθ we can use ratio of x-x1 and y-y1 .

Q: cos r V1+ cos² x d dy sin

A: The integration with respect to 2 variables is carried out by integrating the inner differential…

Q: 1. Integrate x tan- (x²) dx. x4 + 1 2. (a) Evaluate cos? x sint x dx. (b) Calculate dx. x² – 5x + 6…

A: These are integrals which can be evaluated using standard techniques. The solution typed in LaTeX…

Q: 元 1 JTC tan a = <a< T; cos ß = 5,0<B<7 12' 2 2 sin (a + B) (b) cos (a + B) (c) sin (x - B) (d) tan…

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Q: Part (a) Let f(t) = tet0t +e sin 19t. Find L{f (t)} %3D Part (b) 2s + 16 Find C'{F(s)} (s +3)° Let F…

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Q: J4 na * (L-X) Cos nx L x dx Hence using: Fourier cosine & Sine Functions

A: Here the integration is given by ∫0Lx2(L-x) cosnπxLdx Using Fourier cosine and sine functions, the…

Q: sin² (t) = cos² (t) + 0.25 sin² (t) - cos² (t) = 0.25 r. a. = where k EZ where k EZ or or t= O where…

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Q: Consider the function y = -2 sin (2x – 7) for -7 < x < 3. (a) State the amplitude, period and phase…

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Q: r(t) = (5 cos (t), 5 sin(t), 3 sin²(t)) at t ¹ (7) = ㅠ 4

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Q: - 2 sin(v) cos(v) – 4 Let h(v) = d Determine dv d dv

A: hv=-2sinvcosv-4

Q: 4. Use appropriate trigonometric identities to determine 1 dx 1- cos? x (i) (ii) Scos 7x dx (ii) S(1…

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Q: Part (a) Let f (t) = te" +e-5t sin 16t. Find L{f (t)} %3D

A: According to the guidelines, we have to solve only the first question, rest of the question should…