Prove that lim 1/(x^3+1)=2 when x approaches 1?

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Answer 1 · 2018-03-28T16:31:05

2

lim #1/(x^3+1)#
lim #1/x^3+1/1#
as x approaches to 0
then,
#1/(1^3)+1#
i.e. 1+1=2
hence proved

Answer 2 · 2018-03-28T16:48:53

#lim_(x -> 1) (frac(1)(x^(3) + 1)) = frac(1)(2)#

We have: #lim_(x -> 1) (frac(1)(x^(3) + 1))#

Let's substitute #1# in place of #x#:

#= frac(1)((1)^(3) + 1)#

#= frac(1)(2)#

So this limit is equal to #frac(1)(2)#, not #2#.