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

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

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

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

- 1

Solution steps

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

Simplify

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

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

Plug in the value

x = 0

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

Simplify

= - 1

ln (3 - x^{3})

\int ln (x^{2} + x + 1) d x

\int 8 sec^{3} (x) d x

\frac{\partial}{\partial y} (x^{2} \cdot ln (y))

4 y^{^{''}} - 6 y^{^{'}} + 7 y = 15

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