What is the limit as x approaches 0 of 9/x-9/(x^2+x) ?

The limit as x approaches 0 of 9/x-9/(x^2+x) is 9

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limit as x approaches 0 of 9/x-9/(x^2+x)

x \to 0 lim (\frac{9}{x} - \frac{9}{x ^{2} + x})

9

Solution steps

x \to 0 lim (\frac{9}{x} - \frac{9}{x ^{2} + x})

Simplify

\frac{9}{x} - \frac{9}{x ^{2} + x} : \frac{9}{x + 1}

= x \to 0 lim (\frac{9}{x + 1})

Plug in the value

x = 0

= \frac{9}{0 + 1}

Simplify

= 9

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

\int_{1}^{2} (x x - 1) d x

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\int \frac{1}{x ^{2} + 8 x + 25} d x

What is the limit as x approaches 0 of 9/x-9/(x^2+x) ?
The limit as x approaches 0 of 9/x-9/(x^2+x) is 9