What is the limit as x approaches 0 of (x^2+x)/(3x) ?

The limit as x approaches 0 of (x^2+x)/(3x) is 1/3

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limit as x approaches 0 of (x^2+x)/(3x)

x \to 0 lim (\frac{x ^{2} + x}{3 x})

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

x \to 0 lim (\frac{x ^{2} + x}{3 x})

Simplify

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

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

Plug in the value

x = 0

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

Simplify

= \frac{1}{3}

x \to - \infty lim (4 e^{x})

x \to - 6 + lim (\frac{∣ x + 6 ∣}{x + 6})

x \to \infty lim (\frac{e ^{x} + sin ( x )}{e ^{x} + cos ( x )})

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

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

What is the limit as x approaches 0 of (x^2+x)/(3x) ?
The limit as x approaches 0 of (x^2+x)/(3x) is 1/3