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

d er i v a t i v e f (x) = 4 + 3 x

\frac{d}{d x} (9^{4 x})

\frac{d}{d x} (cot^{8} (x))

\int \frac{x ^{2}}{( x ^{2} - 1 ) ^{2}} d x

in v erse l a pl a ce - \frac{1}{s ^{4}}

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