What is the limit as x approaches 0 of (1/(-3+x)+1/3)/x ?

The limit as x approaches 0 of (1/(-3+x)+1/3)/x is -1/9

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limit as x approaches 0 of (1/(-3+x)+1/3)/x

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

- \frac{1}{9}

Decimal

- 0.11111 \dots

Solution steps

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

Simplify

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

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

Plug in the value

x = 0

= \frac{1}{3 ( 0 - 3 )}

Simplify

= - \frac{1}{9}

n \to \infty lim (1 + \frac{3}{n})

x \to 0 + lim (x^{2} lo g_{e} (x))

x \to - 1 lim (3 x^{2} - 5)

x \to 0 lim (x ln ∣ 9 x ∣)

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

What is the limit as x approaches 0 of (1/(-3+x)+1/3)/x ?
The limit as x approaches 0 of (1/(-3+x)+1/3)/x is -1/9