# Integration and convergence

When representing a function as a power series, why do we evaluate the constant C of integration at 0 to determine the value of C?

Also, if the limit of a function is 0, does that mean that the function itself converges to 0?

HallsofIvy
Homework Helper
When representing a function as a power series, why do we evaluate the constant C of integration at 0 to determine the value of C?
What does "representing a function as a power series" have to do with integrating? The most common way of writing a function as a power series is the Taylor's series method that involves differentiation. Could you give a specific example of what you are talking about?

Also, if the limit of a function is 0, does that mean that the function itself converges to 0?
What do you mean by "function itself converges to 0"? "Convergence" always implies a limit. Do you mean the value of the function is 0?

If the limit, as x goes to a, of f(x) is any specific value L (which could be 0) and f is continuous at a, then, yes, f(a)= L. That is the definition of "continuous".

For the first question I am just referring to when figuring out the constant C from an indefinite integral, is the protocol to plug in zero into f(x) to see what the value of C is?

Gib Z
Homework Helper
Not always, 0 may be the most convenient but any point within the domain of the function can be used. Sometimes 0 is not in the domain.