abhijeetp5
May 6, 2010, 09:40 PM
Hi All,
I was going through basic definition of limts wherein it is defined that
Limit of a function f(x) is said to be L iff,
|f(x) - L| > 0 whenever |x-a|>0
Source:
http://web.mit.edu/wwmath/calculus/limits/formal.html
meaning when 'x' is not 'a' then limit of f(x) at 'a' and value of f(x) at 'x' are also not equal.
consider the following example:
f(x) = x/x
this function is undefine at x=0;
Limt f(x) = 1
x->0
here a = 0
checking the above definition,
consider x = 1 , x!= a hence |x-a| >0
f(1) = 1 = L hence |f(x) - L|= 0 even if |x-a| >0
This is confusing me. Please guide.Please Rectify if I went wrong somewhere.
I was going through basic definition of limts wherein it is defined that
Limit of a function f(x) is said to be L iff,
|f(x) - L| > 0 whenever |x-a|>0
Source:
http://web.mit.edu/wwmath/calculus/limits/formal.html
meaning when 'x' is not 'a' then limit of f(x) at 'a' and value of f(x) at 'x' are also not equal.
consider the following example:
f(x) = x/x
this function is undefine at x=0;
Limt f(x) = 1
x->0
here a = 0
checking the above definition,
consider x = 1 , x!= a hence |x-a| >0
f(1) = 1 = L hence |f(x) - L|= 0 even if |x-a| >0
This is confusing me. Please guide.Please Rectify if I went wrong somewhere.