By Deepak Bhardwaj

ISBN-10: 8131803112

ISBN-13: 9788131803110

This e-book relies at the most up-to-date syllabus prescribed through quite a few kingdom forums. The publication is perfect for intermediate sessions in colleges and faculties. It includes of Cartesian procedure of oblong Co-ordinates, instantly strains, Circle, Parabola, Hyperbola, Ellipse and advent to 3 Dimensional Co-ordinate Geometry.The salient positive factors of the publication are: it's been divided into 8 chapters. In every one bankruptcy, all strategies and definitions were mentioned intimately; a good number of well-graded solved examples are given in each one bankruptcy to demonstrate the thoughts and techniques; the comments and notes were extra in general within the booklet in order that they can help in figuring out the guidelines in a greater manner; on the finish of every bankruptcy, a quick workout has been included for the short revision of the bankruptcy; all suggestions are written in uncomplicated and lucid language; the publication will consultant the scholars in a formal method and encourage them evidently and excellent good fortune; and the e-book serves the aim of textual content in addition to a helpbook

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Both sn and s,1tend to the same limit s. 53 (i), lim u„ exists and lim u„ = s—s = O. I Note carefully that the converse of (3) is false. The example un, = 1In shows that it is possible to have lim un = 0 and Zun divergent. In other words (see exercise 2 (g), 1) The condition lim un = 0 is necessary but not sufficient for the convergence of Zun. (4) If Eunis convergent, then so is any series whose terms are obtained by bracketing the terms of Zunin any manner, and the two series have the same sum.

Un or, more shortly, sn =Fur. If, as n co, sntends to a finite limit s, we say that the infinite series urF u2 + + or E unconverges (or, is convergent) and that s is its sum. The number unis the nth term of the infinite series and sn is the sum of the first n terms. ) You should note carefully that, when applied to infinite series, the meaning of the word sum has been widened from its use in algebra. Hitherto it has meant the number which is got by adding the numbers contained in some given finite set.

Continuous functions The reader will have acquired from examples the impression that the common functions can reasonably be called continuous, though some of them may present discontinuities for particular values of x. 3 as being continuous except at x = 2 and x = 4. He would think of a function as continuous so long as its graph can be drawn without taking the pencil off the paper. We must now refine these rough ideas into analytical concepts. The reader, after reflection, will (we hope) agree that for a function f to be continuous at a value x = c he requires that (1) f(c) is defined, (2) as x approaches c, the value of f(x) approaches f(c).

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