Could someone please check my work

Using any of the results in this section, prove the following. 1. lim - = 0. 1 1 + 3n 0, 3N E N so that Vn > N, 1 + 3n Given & > 0, take N E N such that NV > - . Then n > N implies that n > n > - , we have 1 n . Thus for n > N we have 1 1 + 3n - 0 = 1+3n 0, 3N E N so that Vn > N, 6n-+5 - - 3 0 , take N E N such that N > max 1 3, . Then n 2 N implies that n > 3 and n > Since n > 3 , we have In + 5 n' . Thus for n > N we have 6n2 + 5 3 2 - 3n = on2 + 5 - 3(2n2 - 3n) = 2n2 - 3n 6n2 +5-6n2 +In = 2n2 - 3n In + 5 12n 12