Question

given f(x) =
{ 2x^2 + 5 x < or equal to 2
3 - x^2 x > 2

find
lim f(x)
x -> 2^+

lim f(x)
x -> 2^-

lim f(x)
x -> 2

Answer 1

given f(x) =
{ 2x^2 + 5 x < or equal to 2
3 - x^2 x > 2
What????
Perhaps you mean:
given f(x) =
2 x^2 + 5 when x < or equal to 2
3 - x^2 when x > 2
if x is slightly bigger than 2
3 - 4 = -1
if x is slightly smaller than 2
OR
if x is 2
then
2(4) + 5 = 8+5 = 13

Answer 2

since the left limit does not equal the right limit, lim as x->2 does not exist.

And of course, f(2) is not even defined.