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: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

A: The given function is fx=sinxx. To find the value of f'π2, first take the logarithmic of fx=sinxx on…

Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

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Q: Express these functions either in terms of a cosine term only and as a sine term only or expand to…

A: Note:-  cosA-B =cos A cos B - sin A sin BsinA+B =sin A cos B + cos A sin B   Part (1):- Given that…

Q: Prove 3sin x-45 in ³x = Sin (3x)

A: To prove that,3 sinx-4 sin3x=sin3x

Q: Show that (a) · J-1;2(x) = 2 Vлx cos x

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Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: Let 7 (t) = < - 2 cos(2t), Find F(t)dt (don't include the +C)

A: Please refer to the image below.

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: [ 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: Solve S(cosa{x – +)<(1 + +) dx -

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Q: dt cos (2 sin 21) /1– 4r

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Q: x-1 6)/2=0²+5² x² - 4x + 5 (1) (k) / zeaz² +b dz dx (i) (2x² – 5) sin x da (1) √²×² = √16x² dx

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Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: We have determined that if we let u = sin(0), then du = cos(0) de on the interval sec¹(8) cos(0)…

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

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Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: sin(2t). Find Əz Ət if z = √r² + s², r = cos(2t) and s =

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Q: d (c) (cos(2²) + In(3 – 2æ)) dx

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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: a) f(4x)dx x)cx

A: ∫02f4xdx Now, solve the above integral, ∫02f4xdx=∫01f4xdx+∫12f4xdx=f4·1-f4·0+f4·2-f4·1=f8-f0=1-0=1…

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 (t) =-e" sin (21 +7)

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: (b) Verify that f(x) = 2 cos(x) sin(1x). f(x) = sin(6x) + sin(7x) = 2 sin = 2 sin 6x + N 2 X COS 6x…

A: Given

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

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: cos(2y) – 3x?y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0 %3D

A: Let's find.

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

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: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 8 8 + 4 sin(3x)cos(3x), sin(2x) +…

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Q: 2.) (3x + x2) sin(2x) dx Use whatever method you want to

A: Part 1