Let x(t) =u(cos(2xt)) - (u(t) -u(t-2)) and h(t) =eu(t), and let y(t) - x(t) h(t). What is the value of y(3) ? Hint: u(x) is the unit step function O y(3) = 0.037437 O None of the choices O I(3) = 0.75193 O y(3) -0.10177 y(3) -0.04408 v(3)-0.32569

Q: Find the inflection point of f (x) = ax – x² + e, where a is a positive constant. O In(3) O None of…

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Q: (A B Which of the following functions satisfy x²dy + y(x + y)dx=0 with y(1) = 1 ? 3x²y = 2x + y x²y…

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Q: 4. Let g be the function given by f(x) = [(3t – 67)dt .What is the x-coordinate of the point of…

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Q: = f(x) = (4x – 2)(x² – 3). F %3D

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Q: [Motion in R³] A drone has an initial position of (3,1, 2) and an initial velocity of (-2,5,1). The…

A: Here we can use the following formula to find displacement function: vt=∫at dtst=∫vt dt

Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

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Q: 1. f(x) = x² 9 2. f(0) = cos(30) g(x) = 4|x|² 3. f(t) = et cos(ut) 4. f(x) = e³x 9 9 9 g(0) = 12…

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Q: Identify two functions, f and g, h(x) =tan(√x) such that h(x)=f(g(x)): ƒ(x)= g(x)=

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Q: Show directly that the given functions are linearly dependent on the real line. That is, find a…

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Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

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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.