What is the limit as x approaches 0 of (2x)/(x^2+4x) ?

The limit as x approaches 0 of (2x)/(x^2+4x) is 1/2

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limit as x approaches 0 of (2x)/(x^2+4x)

x \to 0 lim (\frac{2 x}{x ^{2} + 4 x})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (\frac{2 x}{x ^{2} + 4 x})

Simplify

\frac{2 x}{x ^{2} + 4 x} : \frac{2}{x + 4}

= x \to 0 lim (\frac{2}{x + 4})

Plug in the value

x = 0

= \frac{2}{0 + 4}

Simplify

\frac{2}{0 + 4} : \frac{1}{2}

= \frac{1}{2}

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

x \to \infty lim (e^{6})

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

x \to \infty lim (\frac{3 x ^{2}}{e ^{x^{2}}})

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

What is the limit as x approaches 0 of (2x)/(x^2+4x) ?
The limit as x approaches 0 of (2x)/(x^2+4x) is 1/2