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

Mar 28, 2018

2

#### Explanation:

lim $\frac{1}{{x}^{3} + 1}$
lim $\frac{1}{x} ^ 3 + \frac{1}{1}$
as x approaches to 0
then,
$\frac{1}{{1}^{3}} + 1$
i.e. 1+1=2
hence proved

Mar 28, 2018

${\lim}_{x \to 1} \left(\frac{1}{{x}^{3} + 1}\right) = \frac{1}{2}$

#### Explanation:

We have: ${\lim}_{x \to 1} \left(\frac{1}{{x}^{3} + 1}\right)$

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

$= \frac{1}{{\left(1\right)}^{3} + 1}$

$= \frac{1}{2}$

So this limit is equal to $\frac{1}{2}$, not $2$.