Question

is lim as x approaches c the same as f(c)?

Answer 1

where is the function f(c)

Answer 2

c=3, f(x)= (x^2+5)/(x-6)
continuous or no?... is the question.

Answer 3

at c=3, yes... the function is defined at x=3 so the limit of f is f(3)

Answer 4

what if x=c is not defined?

Answer 5

if f(x) is not defined at x=c, then the limit can still exist but not necessarily at f(c).
also, if there is a vertical asymptote at x=c, then the limit does not exist.

Answer 6

the limit can still exist but not necessarily at f(c)?

Answer 7

yes... for example...

here, the limit of f(x) as x approaches c is a.... NOT f(c)