Question

If the limit as x-> 3 of f(x)=7 which of the following must be true?
1. f is continuous at x=3
2. f is differentiable at x=3
3. f(3) = 7

why would the answer to this question be "none"?

Answer 1

well look at the definition of a limit

Answer 2

i would say the answer is none, because :
1: function is continuous at x=3 if bouth side limits are equal to the value of the function at the point
2: function can have a limit at the point , even be continuous ,without being diffrentiable at it.
3: similar to part 1, we know nothing about the actual value of the function at a x=3 onlñy from the limit

Answer 3

none of them is true see below

Answer 4

thanks everyone!!