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

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

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

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

- 4

Solution steps

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

Simplify

\frac{4}{x ^{2} + x} - \frac{4}{x} : - \frac{4}{x + 1}

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

Plug in the value

x = 0

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

Simplify

= - 4

\int (5 - x^{4} - e^{2 x}) d x

\frac{d}{d x} (2 cos (x) sin (x))

\frac{d}{d x} (g (x) (x)^{2} (x))

2 x e^{x} + x^{2} e^{x}

200 x - \frac{x ^{2}}{30}

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