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

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

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

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

- \infty

Solution steps

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

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

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

x \to - 1 + lim (x) = - 1

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

= (- 1) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

f (x) = - 0.04 x^{4} + 4

f (x) = arctan (e^{2 x})

\frac{2 x}{x ^{2} - 8}

(5 y - 2 x) y^{^{'}} + 2 y = 0

n = 1 \sum \infty (1 - \frac{2}{n})^{n}

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