Lim(ln(e^x-1))/x, as x goes to +infinity ?

1 Answer
NJ
Apr 6, 2018

#lim_(x->oo) ln(e^x-1)/x = 1#

Explanation:

#lim_(x->oo) ln(e^x-1)/x#

#=lim_(x->oo) (d/(dx)ln(e^x-1))/(d/(dx)x)#

# = lim_(x->oo) e^x/(e^x-1)#

#=lim_(x->oo) (d/(dx)e^x)/(d/(dx)(e^x-1))#

#= lim_(x->oo) cancel(e^x)/cancel(e^x) #

#= lim_(x->oo) 1 = 1#

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