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

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

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

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

- 1

Solution steps

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

Simplify

\frac{\frac{1}{x + 1} - 1}{x} : - \frac{1}{x + 1}

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

Plug in the value

x = 0

= - \frac{1}{0 + 1}

Simplify

= - 1

x^{7 x}

\int cos (x) (1 + 5 sin^{2} (x)) d x

n = 0 \sum \infty \frac{1}{n ^{2} + n + 1}

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

\int 2 e^{- 2 x} d x

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