What is the limit as x approaches-3 of (\frac{x+3)/(3x)}{x^3+27} ?

The limit as x approaches-3 of (\frac{x+3)/(3x)}{x^3+27} is -1/243

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limit as x approaches-3 of (\frac{x+3)/(3x)}{x^3+27}

x \to - 3 lim (\frac{\frac{x + 3}{3 x}}{x ^{3} + 27})

- \frac{1}{243}

Decimal Notation

- 0.00411 \dots

Solution steps

x \to - 3 lim (\frac{\frac{x + 3}{3 x}}{x ^{3} + 27})

Simplify

\frac{\frac{x + 3}{3 x}}{x ^{3} + 27} : \frac{1}{3 x ( x ^{2} - 3 x + 9 )}

= x \to - 3 lim (\frac{1}{3 x ( x ^{2} - 3 x + 9 )})

Plug in the value

x = - 3

= \frac{1}{3 ( - 3 ) ( ( - 3 ) ^{2} - 3 ( - 3 ) + 9 )}

Simplify

\frac{1}{3 ( - 3 ) ( ( - 3 ) ^{2} - 3 ( - 3 ) + 9 )} : - \frac{1}{243}

= - \frac{1}{243}

x \to 0 lim ((1 - x)^{\frac{3}{x}})

x \to - 2 lim (\frac{- 8}{x ^{2} - 4})

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

x \to 4 lim (\frac{x ^{2} - 4}{x + 2})

x \to 2 lim (x^{4} - \frac{1}{2})

What is the limit as x approaches-3 of (\frac{x+3)/(3x)}{x^3+27} ?
The limit as x approaches-3 of (\frac{x+3)/(3x)}{x^3+27} is -1/243