Mathquery

          Welcome To Mathquery         In mathematics continuity and derivability or differentiability plays an important role . So let us discuss it . Definition Of Continuity Of A Function :-         Let f be a function defined on an interval [a,b] . We shall now consider the behaviour of f at points of [a,b] . Continuity At A Point :   Definition(Continuity At An Internal Point) :          A function f is said to be continuous at a point c , a<c<b , if                      lim f(x) = f(c)                    x-->c    In other words , the function is continuous at c , if for each ε>0 , there exists δ>0 such that               |f(x) - f(c) | < ε , when |x-c|<δ Here lim f(x) is called the limit of a function          x-->c  i.e. the function exists when x tends to c. (i)  A function f is said to be continuous from   the left at c if                 lim f(x) = f(c)              x-->c-0 (ii)  Als