Prove the statement using the ε, δ definition of a limit. limaGiven ε > 0, we need δ ---Select--- such that if 0 < |x − 1| < δ, then 13 + 2x 5 − 3 ---Select--- . But 13 + 2x 5 − 3 < ε ⇔ 2x − 2 5 < ε ⇔ 2 5 |x − 1| < ε ⇔ |x − 1| < ---Select--- . So if we choose δ = ---Select--- , then 0 < |x − 1| < δ ⇒ 13 + 2x 5 − 3 < ε. Thus, lim x → 1 13 + 2x 5 = 3 by the definition of a limit. x → 1 13 + 2x 5 = 3.