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

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

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

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

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

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

Simplify

\frac{2 x}{x ^{2} + 3 x} : \frac{2}{x + 3}

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

Plug in the value

x = 0

= \frac{2}{0 + 3}

Simplify

= \frac{2}{3}

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

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

x \to \infty lim (16)

x \to 0 lim (1^{x})

z \to 2 i lim (z^{2} + 3 z)

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