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

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

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limit as x approaches 0 of (4/(1+x)-4)/x

x \to 0 lim (\frac{\frac{4}{1 + x} - 4}{x})

- 4

Solution steps

x \to 0 lim (\frac{\frac{4}{1 + x} - 4}{x})

Simplify

\frac{\frac{4}{1 + x} - 4}{x} : - \frac{4}{1 + x}

= x \to 0 lim (- \frac{4}{1 + x})

Plug in the value

x = 0

= - \frac{4}{1 + 0}

Simplify

= - 4

\frac{\partial}{\partial x} (\frac{14 x}{7 x ^{2} + y ^{2} + 2})

\int_{0}^{1} \frac{1}{x + 2} d x

\frac{7 s + 4}{2 s ^{2} + 16 s + 30}

\frac{x - 2}{x ^{2} - 4}

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

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