true or false: if lim x?0 f(x) = 5 then f(0) = 5

Question

a true and false question referring to limits

Answer 1

The answer is FALSE.

 

For example, let f(x)=(x² + 5x)/x (graph has a "hole" when x = 0)

 

lim f(x) as x→0

 

= lim [x(x+5)/x] as x→0 

 

= lim(x + 5) as x → 0 

 

= 5

 

But, f(x) = x(x+5)/x is undefined when x = 0.