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: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: (1) Let g(x) :| f(t) dt. What is g'(x)? a

A:

Q: Q1. Consider a periodic signal -1 <t<0 S-4, x(t) = 2, 0 <t < 2 with period T=3. a) Draw x(t). dx(t)…

A: Given: A periodic signal with period T=3.

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A: Solution :-

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A:

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: Let h(x) = tan(2x + 3). Then h' (2) is and h'' (2) is

A: given function    h(x)=tan(2x+3)

Q: Salve the fallainequations mithont

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Q: dy 5. dt = e&-t)secy(1+ t²). %3D

A:

Q: Let 7(t) = Find '(t) F (t) =

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Q: 28) y = tan² 2 29) y = In ln x 30) y = (x In æ)²

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A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

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

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Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)

Q: a function y = f(x) be implicitly given by the equation y²-x²y³ - cos (πy) = xª. The point (-1,1).

A: Topic:- application of derivatives

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.