Prove the statement using the ε, & definition of a limit. 2(4+1x) = 5 lim X-2 Given > > 0, we need ---Select---such that if 0 < x 21 <8, then (4+ x) - <-> -x- <-> |||||× - 2 | <= = |x − 2| < |--Select--- ▼ (4+2)-54 12 (4+ 1/2x) = lim x-2 = 5 by the definition of a limit. Illustrate with a diagram. -5---Select-- ▼ . But So if we choose = ---Select--- ▼ 5+8 5 5-8 5+€ 5 5-€ 2-€ 2 2+€ x 5+€ 5 5-€ 5+8 5 5-8 2-8 2 2+8 2-8 2+8 2-€ 2+€ then 0 < x 21 < 6➡ |(4+3x)-542 -5. Thus, x x