What is the limit of #xe^(1/x) - x# as x approaches infinity?
1 Answer
Oct 24, 2016
Explanation:
#=lim_(x->oo)(e^(1/x)-1)/(1/x)#
Direct substitution here produces a
#=lim_(x->oo)(d/dx(e^(1/x)-1))/(d/dx1/x)#
#=lim_(x->oo)(e^(1/x)(-1/x^2))/(-1/x^2)#
#=lim_(x->oo)e^(1/x)#
#=e^(1/oo)#
#=e^0#
#=1#
