devotion & mathematics

              DOUBLE INTEGRALS               The line integrals are often used to find the lengths of the curves i.e if we talk about a circle the line integral is the circumference of the circle or semi circle or quarter circle etc. If we ask about the length of the curve on the circle which is not a complete circle or semi or quarte circle , we chose the part of the circumference of the circle then we need some procedure or  theory to find the length of the curve which are called the line integrals.          This process of line integration is applicable not only for the circles but also for any one or two or three dimensional regular  and irregular shapes .        So what about the surface area of circular cake in a rounded plate or cool drink bottle looks like a cylinder  or football like a sphere etc. In mathematics there are certain formulae for the ab...

                                                  AREA OFSUBSETS OF R 2 Area of a Rectangle in R 2   :                             In R 2 , the rectangle is defined as the set {(x, y)/a≤ x ≤ b, c≤ y≤ d}.                                                    The area is (b-a)(d-c). Area of a bounded subset in  R 2   which is not a rectangle :                                               ...

  CONTENTS : Theorem  * : Cantor's  Intersection Theorem Theorem ** :  Let {x n } be a sequence in a metric space (X,d). For each positive integer n, write                                          E  n ={x  m /n ≥ m}. Then { x  n } is a Cauchy sequence in X if and only if lim diamE n =0. Theorem *** :  For any subset E of a metric space (X,d), diam E=diam Ē. proofs : Theorem * :    Theorem ** :  Theorem *** :                    people also ask :  1. What is a metric space?  2. What is a pseudo-metric?  3. What are meant by open and closed sets?  4. What is a perfect set?  5. What is an interior of a set?  6. What are axioms of real numbers?  #cantor #intersection #theorem  #sequence #diameter #cauchy People also search for Iit ma...