Question

find the indicated limit, if it exists
lim(x->0) f(x), f(x)={5x-9 if x<0
{|2-x| if x>(orequalto)0

-9
-7
2
limit doesnt exist

Answer 1

The limit does not exist.

Although at the 0 the value of f(x) would be 2, the limit asks what the two sides are approaching. From the right (postive) side, f(x) is approaching 2 as x goes to 0. However, the left (negative side) is approaching -9 as it x goes to 0. Therefore, because of this discrepancy, the limit does not exist.