Could someone please check my work

Find The following limit using The limit laws 3. lin ( 10n + 1/A) )= lim /10n + " 9 5+ 2n 9+ 2 = lim 10n + is by Theorem 4.2.1 (d ) lim 9 + 7 = 10limn + 11 lima by Theorem 4.2. 1 ( 6 ) 9 + 21im 4 = 10 ( 1im n) + 11(0) by exercise 4.1. 6 9 + 2 lim -4 Since lim 12 = 0 by example 4.1.6(6), Then by Theorem 4.2. 1 ( c), lime (4 ) = lim ( ,3 . ) = lim . . lime = = 0.0= 0 Since lim (14 )=0 = 10 ( limn ) +0 9+ 2(0 ) = 10 /im n 9 = Do