math

1.  Brief history of Calculus>>>>>>>>>>>>>>>>>>
   In the year of 1668,a german philosphic as well as mathematician named Gotfrid Vilhelm Lajbnic published a full description on calculus. It is he, who gave name of it      as Calculus. Although scientist Isaac Newton discovered it several years ago, he published it in 1693 and published its full description in 1704, 20 years after    Leibnitzs publication. Orginally, Leibnitzs intigral calculus was later adopted acros the country. There is controversies about who discovered calculus.
   Newton himself avoids the debate. Then it is written about who discoverd it. Surprisingly, most of Newton's article were his own. Newton, as president of Royal Society,    formed an impartial committee to end the dispute over inventions. From this committee it is said that they will end the dispute regarding the detector. This committee    began functioning in full force in 1711.The Royal society reports that Leibnitz was accused of stealing research papers. Newton then wrote anonymously
   in favor of the Royal Society's report. After the dead of Leibnitz, Newton said that he found peace by breaking Leibnitz mind.......
2.
3. What does calculus deals with>>>>>>>>>>>>>>>>>
   Calculus has two major branches. One is "Differential calculus", and other is "Integral calculus".
   Differential calculus deals with instantaneous rates of change and the slope of curves. The integral
   calculus concerns accumulation of quantities and areas under or between curvature.
   Calculus invented for the specific purpose of describing the dynamic nature of our universe. To put
   it simply, calculus the maths of motion and change.
   Example :
            By using calculus, we have the ability to find the effects of changing conditions on a
            system like the weather for example. In the atmosphere, we have a changing tem[erature
            and changing pressure. So by using differential equation, metorologists can indicate and
            predict the weather for our benefit........
4. Existence of limit, Continuity and differentiability of a function>>>>>>>>>
   About limit>>>>>
   There are uses of limit in calculus. limits are essential to calculus and are used to define
    continuity, derivatives and integrals.
   In formulas, a limit of a function is usually written as
         lim f(x) = L    ....
         x->c
  suppose 'f' is a real valued function and c is a real number. Intuitively speaking, the expression
  means that f(x) can be made to be as close to 'L' as desired by making 'x' sufficiently close to 'c'....
  About Continuity>>>>>>
   A function f(x) is said to be continous at x=a. If limit exists at x=a, then limiting value will be
   equal to functional value.
   Like  Lim f(x) = Lim f(x) = f(a).
         x->a(+)    x->a(-)
  About Differentiability>>>>>
  A function f(x) is said to be differentiable at a point x=a, if
  Rf'(a) = Lim  {f(a+h)-f(a)}/h and Lf'(a) = Lim  {f(a-h)-f(a)}/(-h)
           h->0                              h->0
  If both existed and have equal values, then it is differentiable.......