Prove the statement using the ε, δ definition of a limit. lim x → 1 4 + 2x 3 = 2 Given ε > 0, we need δ ---Select--- such that if 0 < |x − 3| < δ, then 2 + 1 3 x − 3 ---Select--- . But 2 + 1 3 x − 3 < ε ⇔ 1 3 x − 1 < ε ⇔ 1 3 |x − 3| < ε ⇔ |x − 3| < ---Select--- . So if we choose δ = ---Select--- then 0 < |x − 3| < δ ⇒ 2 + 1 3 x − 3 < ε. Thus, lim x → 3 2 + 1 3 x = 3 by the definition of a limit.