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

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

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

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

\infty

Solution steps

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

Factor out

3 x

from

3 x + 3 : 3 x (1 + \frac{3}{3 x})

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

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

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

Simplify

\frac{x ^{3}}{x ( 1 + \frac{3}{3 x} )} : \frac{x ^{3}}{x + 1}

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

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

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

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

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

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

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

= \frac{1}{3} (- 1) (- \infty)

Apply Infinity Property:

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

= \infty

3 x^{4}

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{x + y})

y = \frac{590}{x}

y = 6 x - x^{2}, y = x^{2} - 2 x

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

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