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

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

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

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

1

Solution steps

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

Simplify

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

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

Plug in the value

x = 0

= \frac{1}{1 - 0}

Simplify

= 1

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

x \to 3 lim (5 x + 8)

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

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

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

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