calc review: can't figure this out

lim    (e^x + x)^(1/x)
x->0+ 

and

lim      (x-pi/2)tanx
x->pi/2+

4

calculus harder

1st one:

lim    (e^x + x)^(1/x)
x->0+


lim   exp( ln( (e^x + x)^(1/x)))
x->0+

Can push the limit inside exp since it's continuous:

exp( lim ln( (e^x + x)^(1/x)))
     x->0+
=
exp( lim (1/x) ln(e^x + x))
     x->0+
Is 0/0, so w/ l'hopital:
exp( lim   e^x+1/e^x+x/1)
     x->0+

= exp(2) = e^2