What is the limit as x approaches-1 of (x+1)/(x^3+1) ?

The limit as x approaches-1 of (x+1)/(x^3+1) is 1/3

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limit as x approaches-1 of (x+1)/(x^3+1)

x \to - 1 lim (\frac{x + 1}{x ^{3} + 1})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to - 1 lim (\frac{x + 1}{x ^{3} + 1})

Simplify

\frac{x + 1}{x ^{3} + 1} : \frac{1}{x ^{2} - x + 1}

= x \to - 1 lim (\frac{1}{x ^{2} - x + 1})

Plug in the value

x = - 1

= \frac{1}{( - 1 ) ^{2} - ( - 1 ) + 1}

Simplify

\frac{1}{( - 1 ) ^{2} - ( - 1 ) + 1} : \frac{1}{3}

= \frac{1}{3}

What is the limit as x approaches-1 of (x+1)/(x^3+1) ?
The limit as x approaches-1 of (x+1)/(x^3+1) is 1/3