# Difference between the value of function at A and the limit

1. Jul 15, 2010

### amaresh92

what is the difference between the value of function at A and the limit of function at A.
to find the limit of function by direct substitution we just put the value A in function which gives the limit.but i think it should give the value of function at that point .how it become limit?

2. Jul 15, 2010

Re: limit

A function may not be defined at some point c, but the limit, as x --> c, may exist. A function whose limit, as x --> c through the domain, exists and equals f(c) is continuous at the point c.

3. Jul 15, 2010

### HallsofIvy

Re: limit

That only works if the function is continuous. In fact it is the definition of continuous:
A function is said to be "continuous at a" if and only if $\lim_{x\to a} f(x)= f(a)$".

Otherwise, there is no relationship at all between f(a) and $\lim_{x\to a} f(x)$.

For example, "f(x)= 3x for x any number except 1 and f(1)= 5" is a perfectly valid function. It's value at x= 1 is 5 but the limit as x goes to 1 is 3.

Last edited by a moderator: Jul 17, 2010