A function f is defined by the following descriptions near x=2:
• For 0<x<2, f(x)=(x−2)21+1.
• For x>2, f(x)=3x−5.
Which of the following is true about x→2limf(x)?
a) The limit exists and equals 1.
b) The limit exists and equals ∞.
c) The limit does not exist because the left-hand limit is unbounded while the right-hand limit is finite.
d) The limit does not exist because the function value at x=2 is undefined.