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

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

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Answer 1 · 2018-03-28T16:31:05

2

Explanation:

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

Answer 2 · 2018-03-28T16:48:53

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

Explanation:

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 $2$ .

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

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