Compute the following limits? Calculus help

Compute the following limits using l'Hospitals rule if approrpriate?

a) lim (x-->1) of [(7^(x)-7)/(x^(2)-1)]

b) lim (x-->infinity) of [( arctan(x)) / ((1/x)-7) ]?

in part a) the lim approaches (7-7)/(1-1) which approaches 0/0 so we can use LHopital

differentiate numerator: 7^x ln 7
differentiate denominator: 2x

as x-> 1, this becomes 7^1 x ln7/2 = 6.81

in part b) there is no indeterminate limit; arctanx => pi/2 as x->infinity

1/x->0 so the fraction becomes pi/2/(-7) -> -0.224