Let X have a p.d. f.f(x) that is positive at x = -1,0,1 and zero elsewhere. (a) If f(0) =, find E(X2). (b) If f(0) = and E(X) =. determine f(-1) and f(1).

Q: Find the function f (x) for which f (x) = e-5x, f (0) = 1.

A: A function is a relation which maps each value in its domain to exactly one value in its range. For…

Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

A:

Q: 6. Let s'+- if + -1 and a # 1 f (æ) if x = -1 if æ = 1 1 (a) Find f (-2). (b) Find f (-1). (c) Find…

A: Answer and explanation is given below

Q: Let (0.30)=(3, 4) and (2₁. y) = (3.4, 4.5). Use the following graph of the function f to find the…

A:

Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: Let ​F(x)=x2− 2 and G(x)=13−x.   Find ​(F•​G)(10​)

A:

Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: For each of the functions y = f (x) described below,find f (2).

A: f(2)

Q: Given f (x) = x³ – 2, find f (x).

A: Given that                   f(x) = x^(4/5) - 2, find f-¹ (x).

Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: Suppose that f′​(x)=2x for all x.   ​a) Find ​f(−4​) if ​f(0)=0. ​b) Find ​f(−4​) if f(2​)=1. ​c)…

A: Suppose that f'x=2x for all x. a To find f-4 if f0=0.b To find f-4 if f2=1.c To find f-4 if f-3=10.

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

A:

Q: Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and f(xy) =…

A:

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

A:

Q: a. Suppose that ƒ(x) = g(x³) + eg(3x) where g' and g" exist. Find f' and f" in terms of g' and g".…

A: Here we have given a composition of a function as given below.

Q: Let f(x) and g(x) be defined as follows: f(x) = 2x+ 1, g(x) = /x-3 What is (fog)(x)?

A:

Q: Let f(x) 1 and g(x) = 4x + 7. Then с — 3 - (f o g)(0) = (f o g)(x) =

A: Given:

Q: Let h(x)=f(g(x)). If g(3)=−4, g′(3)=5, f(−4)=−6, and f′(−4)=4, find h′(3). Do not include "h′(3)="…

A: We have to find derivative of h(x) at x=3 .Information is given below:

Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

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.