a) Let (X..A, a) be a mensure space and let J.g: X-Rbe two mensurable functions. Prove that the funetions f+g and fg are measurable. b) Let (X..A) be a measure space and suppose the A, Ag, EA such that A, 1 A (A, A - And A-r A). Prove that if a(A)

Q: Let f: A→B be a function. Prove or disprove the equivalence: (a) f is injective (b) If C is any set…

A:

Q: Let S be set of all strings of a's and b's. Define a relation R on S as follows: Vs, t E S, sRt e…

A: Let A be any and let R be any binary relation on the set A. Relation R is symmetric if for a, b∈R,…

Q: Suppose that functions digih. domain that and Jrg we have continuous. i with the some codomain such…

A:

Q: Let (X, E) be a measurable space and (En) be a sequence of pairwise disjoint sets in E. If, for each…

A: Given X,∑ is a measurable space and En  be a sequence of pairwise disjoint sets in ∑. Given f is…

Q: consider the space generated by the set of functions {cos nx , sen nx} with ,n = 0,1,2, … show that…

A: We will prove  the given statement.

Q: Let fex) and g(x) be two (Piece - wi'se) comtinuous functions on Intervál caib]. Then if t) ¿gCx)…

A:

Q: Prove that the Peano Curve is continuous and surjective mapping [0,1] onto the unit square

A:

Q: b) Compute Re fli) when : f(2)= √Z - 1² and f(0) = -i c) Which of the following functions are…

A: Analytic function : A function f is analytic at a point complex point z=a iff the f(a) is a finite…

Q: Provide two disjoint nonempty open sets C, D. Is it possible for a function g : R → R to be…

A: A set is a collection of elements like, numbers, objects. The numbers can be called as set of real…

Q: continous real valued function 58) Let f be a that the set inverse image with respect to f of an on…

A:

Q: sub parts to be solved  g) If A is a set of real numbers that is not open, then A is closed. h)…

A: g) If A is a set of real numbers that is not open, then A is closed.

Q: What is true about the function *) - as *-* ? A) B)(x)→0 from below OC) f(x) is undefined OD)x)→…

A:

Q: let (x, m) be a measurable space. then ¥8:% [, o] are measural ble funetion, then ) I +9 is mea…

A:

Q: Prove that if f : R → R is continuous, then the image of a bounded set over f is bounded.

A: Given f:R->R is continuous function  Let A is bounded subset of R  So the limit point set A' is…

Q: et V be th

A:

Q: Show that in R with the usual topology, the only open sets connected by trajectories are the open…

A: Given that R with the usual topology  A collection of of subsets of R which can be expressed as a…

Q: Let 4=fcx)=3x"+4x' De termine the toltuing: a) Find au points of infiection luse concavity test and…

A: Concept introduction: An inflection point is a point on the graph at which the second derivative…

Q: Let f:X → Y and g:Y → Z are functions show that a) If g of is surjective then g is surjective b) If…

A:

Q: -1) a) Prove that f(z) = 3x+y +i (3y-x) is analytic in & namely: entire b) Prove that if f(z) and…

A:

Q: Exercises 3,5,8 de M 1. Let X be the space of real numbers with the usual topology, and let f: X- X…

A:

Q: Which functions are one-to-one? Which functions are onto? Describe the inverse function for any…

A: One to one: A function f : A → B is one-to-one if for each b ∈ B there is at most one a ∈ A with…

Q: Let f = u + iv be analytic in the connected open set and assume u and v satisfy u? + 3v2 = 4. Show f…

A:

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.