1, 1< |t| < 3; x(t) = -2, |t| < 1 i) Sketch x(t) over [-3,3] and verify that Xo = 0. %3D ii) Sketch the signal y(t)which has the same period and is such that 1, k = 0 -j(nk/3)-1Xx, k + 0 (There is no need to derive X.)

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A: Given, f(x) = (x-1)ex

Q: S Q16) L−¹ {(8 − 1)² + 4) (A) et [cost + sin t] (D) et [cos 2t+sin 2t] (B) et [cos 2t + sin 2t] (E)…

A:

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A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

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

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A: Given: x=-3+cos(t)y=1+sin(t)

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

A: we have to find Laplace transform

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A:

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A: Let B={sin2x,1-cos(2x)}.

Q: 2 -JM 3 0 5 Determine whether v is in the range of T. Fully justify your answer. 1 -2 -1 Let A = =…

A:

Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

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Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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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: 1) Find the fundamental period of the function u + v, if any, by examining whether the functions u…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: 2) Consider the function f(x) = -x + sin(-x) on the interval [0,1]. a) Approximate a root of f using…

A: Given function is              rewrite the above equation as               compare this with…

Q: I need help with this problem becuase I don't know

A: GivenGradient of  is

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: 4) dependent Show that the following set of functions is Linearly independent or linearly f₂(x) = 3,…

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Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

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Q: erfind the first agd decond derivatives oh the funchan

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Q: e/min. hole on Consider a large filled with 10 l of liquid. tank at time tank that is initia Liquid…

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Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,

Q: (1) Let f(x) = 1,x > 0 with domf= R4+. Find the conjugate of function f(x). %3D

A: given fx=1x , x&gt;0 with domf=R++ claim- find the conjugate of function fx

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: x²+4 Let: f(x)= - 16x f'(x) = - f"(x)= 16(3x2+4) x² –4° (x²–4)² ' (x² –4)° 5. Sketch the graph of f,…

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Q: 3) Find the Frenet (TNB) frame for the function at the point (2, 5n,0). Hint: once you find T and N,…

A: Given that  r(t)=-2cos3t,5t,2sin3t The formula for T is, T=r'r', Take the derivative for r,…

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A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.