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

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

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limit as x approaches 0 of x/((1+x)^2-1)

x \to 0 lim (\frac{x}{( 1 + x ) ^{2} - 1})

\frac{1}{2}

Decimal

0.5

Solution steps

x \to 0 lim (\frac{x}{( 1 + x ) ^{2} - 1})

Simplify

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

= x \to 0 lim (\frac{1}{x + 2})

Plug in the value

x = 0

= \frac{1}{0 + 2}

Simplify

= \frac{1}{2}

x \to 0 - lim (2 x + 2)

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

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

n \to \infty lim (\frac{( 2 n + 1 ) ^{2}}{2 n ^{2} + n ^{4} + 2})

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

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