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

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

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

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

1

Solution steps

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

Simplify

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

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

\int_{0}^{2} 8 e^{- 3 x} d x

x \to - 3 lim (9 - x^{2})

k = 0 \sum \infty 3 (\frac{x}{4})^{k}

(\frac{x ^{2} + 1}{x ^{2} - 1})^{3}

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