What is the limit as x approaches-1-of (x^2)/(1+x^3) ?

The limit as x approaches-1-of (x^2)/(1+x^3) is -infinity

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limit as x approaches-1-of (x^2)/(1+x^3)

x \to - 1 - lim (\frac{x ^{2}}{1 + x ^{3}})

- \infty

Solution steps

x \to - 1 - lim (\frac{x ^{2}}{1 + x ^{3}})

\frac{x ^{2}}{1 + x ^{3}} = x^{2} \frac{1}{1 + x ^{3}}

= x \to - 1 - lim (x^{2} \frac{1}{1 + x ^{3}})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to - 1 - lim (x^{2}) \cdot x \to - 1 - lim (\frac{1}{1 + x ^{3}})

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

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

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

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What is the limit as x approaches-1-of (x^2)/(1+x^3) ?
The limit as x approaches-1-of (x^2)/(1+x^3) is -infinity