What is the limit of #((1)/(x))-((1)/(e^(x)-1))# as x approaches infinity?
1 Answer
Jun 13, 2017
If two limits added together individually approach 0, the whole thing approaches 0.
Use the property that limits distribute over addition and subtraction.
#=> lim_(x->oo) 1/x - lim_(x->oo) 1/(e^x - 1)#
The first limit is trivial;
#=> color(blue)(lim_(x->oo) 1/x - 1/(e^x - 1))#
#= 1/oo - 1/(oo - cancel(1)^"small")#
#= 0 - 0 = color(blue)(0)#