Use the Laplace transform to solve the initial-value problem: b) (x) = cos(3x)+sin(3x) - 13³ e-³x 3x y(x) = cos(3x)+sin(3x) 3 y(x) = cos(3x)+sin (3x) d) y(x)-2 cos(3x) + 4 e) f) [y+3y=2 cos(3x), y(0)=4] y(x)=2 cos(3x) - 4 e³x None of the above. -3x + x) + 1/16²³x

Q: Evaluate (x2 + 1) cosx dx O (x2 + 1) sin x + 2x cos x – 2 sin x + C - (x2 + 1) sin x – 2x cos x + 2…

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Q: Find the Fourier coefficients of the periodic function f(x)=x-2x², (-<x<n); f(x+2) = f(x)

A: We have to solve by Fourier series.

Q: -3 if 0 6 The Fourier sine transform of f(x) is sin 3w a) 6 2 (sin 6w b) -3 1-cos 6w с) —3 -cos 3w…

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: Let f(x) = sin(2x) + cos(x) then f"(x) Select one: O a. 4sin(2z) + cos(z) O b. -sin(2x) – cos(x) Oc…

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Q: If g (t) = sint dt, then g'(x): Sva 2t sin √x 4x sin x 2x sin √x 2√x COS 4 x None of these =

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Q: [sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x); [cos(2x) – 1]+ +C + 12 8 4 sin(3x)cos(3x)…

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Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: Compute the derivative of f(x) = ( sin(2x + 1))/°. 4 (sin(2x+ 3 1) -1/3 • cos (2x + 1) 4 -1/3…

A: Given

Q: Match the graphs with their parametric equations. I O (a) x=4-t+2, y = ² O (b)x= 2 - 3t, y = √t O…

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: The derivative of f (#) cos(-2 a +a - a2 - 2 a +1) is O f (a) = (8 a° – 3 a? +2 a + 2) sin (-8 a + 3…

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find y as a function of t if 4y" +12y +9y = 0, y(0) = 6, y(0) = 6. 42 y(t) = 6 cos(-¹)+sin(-)

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Q: Let f(x)=2 cos(5x)+3 sin(4x) and let q, be the Fourier polynomial of degree n for f. (a) Show that…

A: Given: fx=2cos5x+3sin4x The period is 2π as f2π+x=fx The fourier polynomial of degree n is:…

Q: Consider the variable coefficient linear homogeneous ODE a(x)y" + b(x)y' + c(x)y = 0 where sin(z)…

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Q: Given that f(x) = 2x + cos(x) is a bijective function, find (f-')'(1)

A: The function f-1 represents the inverse of function f. Therefore, if f-1x=y then x=fy represents the…

Q: Suppose f(t)dt = 2 + x' + 3x°- cos(x'). Find f(x) for x > 0. %3D O f(x) = 1 + 6x² + sin(x²) O f(x) =…

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Q: Tx/2+sin(ix) f(x) = V2r then = (x).

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Q: J sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) , sin(2x)cos(2x) , sin(2x) + + C 12 8 8 4 sin(6x)_ sin(2x)…

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Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: f, (3,5) and fy (3,)us(«, y) = |and f, (3,) if f (x, y) = (b) Find x² sin(y) – Ax-3 10 CLO-2 Where A…

A: The given function is  f(x, y) = x2. siny - Ax-3

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: Integrate the function. 181-x? V81 -x² dx 11x V81 -x² In 11 V81- x? +C 2. O A. 11 O B. 181 -x2 In 11…

A: Correct option (A)

Q: (a) Find of: dx (i) e? – x y = cos(2x) (ii) y = (V4x2 + 1 – 5x)

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Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

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