Laplace transform of x(t) = cos(4f)u(t) %3D 16 X (s) = s* +16 4 X (s) = s* +16 X(s)D s? +4 X(s) = s´ +16

Q: Let r(t) = Find f(t)dt ( )dt (don't include the +C) fF(t)dt = <[ Calculator 1 Check Answer

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Q: 2. Start: y= x What transformations occurred? End: y =-9(x-8)² + 5

A: First   shift the graph right by 8 units.  Then  strecth by (-9) units.  Then  shift upward by 5…

Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: 1 f(x) = 5 sin (-x - π)

A:

Q: Which transformation includes a reflection of f(x) = (x − 1)² + 1 over the x-axis? O f'(x) = (2x −…

A: f(X) = (x-1)2+1

Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

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Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: 6. Evaluate * у" + 9у 3 0; у(0) — 2 , у'(0) %3D 9 2cos3t + 9sin3t 2cos9t + sin9t А. В. 2cos3t +…

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Q: 23. Integrate: S x+2 dx 2 A. V1– x² + Sin-1x + C C. -V1– x² +Sin-1x + C B.V1 – x2 +Sin-1x + C D. –V1…

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Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: se-2s -)=D 's²+45+3

A: Given,

Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: dx S (x² – 6x + 13)² 4.

A:

Q: The characteristic equation of the ODE y (3) -2y'+y?=0 is defined by

A: Giveny(3)-2y'+y2=0

Q: 29. 1 + dx + /2r

A:

Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: How do i find e(x), var(x) and e(x^3) using the moment generating function

A: Let us define the random variable X with moment generating function Mx(t).The moment generating…

Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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Q: Find Solution of Homogeneous linear ODE s (D°, 60 +131 Jy

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Q: Performing iterations on (25) respectively, leads to the following: n-1 X2km+j v; II n-1 Y2km+j…

A: Given: 2km+j=2km+j2+rj To find: Corresponding equation

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: Find the Laplace transform g(t)={0  0≤t<5 ;(t-5)^2 t≥5 A. (e ^ (- 5s))/(s ^ 3) B. (2e ^8s)/(s ^…

A: Solution:

Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: 6. dx = x + 4x + 5 (A) arctan(x + 2) + C (B) arcsin (x + 2) + C (C) In|r*+ + 4x + + C 1 (D) + C x° +…

A: Proceed as shown below...

Q: 50, dex(+) = -25 (+ + 2) + 25 (1-0) + 15 (t-1) at 2 = -√(x + 2) + 251f) + 5lt-2) By using…

A:

Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)

Q: d[cos(x*)] dx (2k+1)! (-1)*2,* - (2k)! .(-1)시2x4~2 (2k+1)! (-1)*2x*-3 E (2k+1)! None (-1)*-'2x*-1 E…

A:

Q: ind the equation of the curve whose y" = ○ y=2 sin-¹ (2) — 4³-√3 -1 - O y = y = sin¯¹(x). X sin (x)…

A:

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: We consider the following 27-periodic function f given by S0, if -n 1. 3- Deduce the Real Fourier…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer three subparts…