Limits, Definition

Question

Always true or false?

1. The value of the limit of f(x) as x approaches e does not exist when e is not part of the domain of f.
2. If f(x) = c, c is all real numbers, then the limit of f(x) as x approaches a is equal to a.

Thank you in advance!

Answer 1

1. False

For example, consider f(x) = (x-e)/(x-e)

This function is defined everywhere except at x=e, yet

the limit f(x) as x->e exists and is equal to 1.

2. The sentence is not grammatically correct, therefore I do not understand its meaning.

I will talk about a different question:

"If f(x) = c, c is any real number, then the limit of f(x) as x approaches a is equal to a."

This is the true only in the special case when a = c.

The following statement is true unconditionally:

"If f(x) = c, c is any real number, then the limit of f(x) as x approaches a is equal to c."