Q.2 Consider the decaying exponential signal f(t) = Ae¯"u(t);a>0 -at 1 where r=- is caled the time constant of f(t). a a) Show that at time t= Nr x(Nr) =: e x(0) , ie., x(Nr)_ 1 x(1 + Nr) - and x(0) x(t) b) Now consider the sinusoidal signal with decaying exponential envelope: x(1) = {Ae" cos(2,f +9)}u(t) ; a>0. Give the relationship between the time period To of the sinusoidal signal and the time constant t of the exponential signal if x(T,) _ 1 x(107,) x(0) =0.01 . %3D x(0)

Q: Part 1 1. If f(0) = g(0) = 0 and f" and g" are continuous, show that ff f(x)g"(x)dx= f(a)g'(a) — ƒ…

A: I have given the answer in the next step. Hope you understand that

Q: 1. Find dy/dx a) y = In (2x² – 3x) %3D b) y = [e" dt ) d) y = In|sec(x)+ tan(x) e) y = 7std*) S)y =…

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Q: Find the inverse of the function. Az) = 0.2* O p'- 1 0.2* O f(x) = logo2x O f'(x) = x°: 02 O fx) =…

A: See attached file for a step by step explanation to find the inverse of the given function.

Q: (11) Let G(x) = | a In(1+t²)dt. (a) Find G(1). (b) Find G'(1). (c) Find G"(1).

A: a) G(1)=0 b) G'(1)=piln(1+x^2)|x=1 G'(1)=pi ln(2) c) G''(x)=pi(1/(1+x^2))2x G''(1)=2pi/2 G"(1)=pi

Q: Q1: Find 1) e (3 + e6t)2 2) l {e-3t (t + 1)²}

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Q: ) prove thaE cos ( x) dx =- T e x" + x2 +l 213

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Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point %3| 2 y = x + y =…

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Q: 2) Find the minimum value of 6 cos x 8 sin x 3) The phase shift o̟ in a certain electric circuit…

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Q: 2. Suppose f(x+3)%3D f(xr), what is the period of the function f ? (A) 4 (B) 3 (C) 2 (D) 1

A: topic - functions

Q: Find F(s). F(s) = L{e-⁹t cos(2t)}

A: We have to find .

Q: Compute all second derivatives of f(1.y) = (x+) e- %3D

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Q: du 4. (a) If u = log(x³ + x*y + y°), prove that x=+y = 3 du (b) If u = tan-' (x² + 3xy + y²) , prove…

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Q: IfI(u) = [log, (1-2u cos x+ u' )dx, then prove that, I(u)+I(-u)-DI(u²).

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Q: 12:06 ■I 5G (3) Calculate the derivative f'(x) of the following function a) f(x) = √1- b) f(x) = x²…

A: Solution of the given question is like as

Q: 20. Let h be the function defined by h(x) = [", sin²r dt. Which of the following is an equation for…

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A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dN + N = Ntet+2 dt

A: we have to solve first order of differential equation given below

Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

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Q: Ex: SOLVE THE D.E. y"+ 2y' + 2y = e-*/cos3x

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.