Find f and a if: lim x->5 ( 2^x - 32)/(x-5)

Answer 1

WE have undterind form 0/0. By L'opital rule

lim x->5 ( 2^x - 32)/(x-5) = lim x->5 ( 2^x - 32)'/(x-5)' =

lim x->5 ( 2^xln2/1) = 2⁵ln2/1 = 32ln2