QuestionAugust 25, 2025

lim _(xarrow 0)(x)/(x^2)-x

lim _(xarrow 0)(x)/(x^2)-x
lim _(xarrow 0)(x)/(x^2)-x

Solution
4.2(171 votes)

Answer

-1 Explanation 1. Simplify the expression Factor the denominator: x^2 - x = x(x - 1). The expression becomes \frac{x}{x(x-1)}. 2. Cancel common factors Cancel x in the numerator and denominator: \frac{1}{x-1}. 3. Evaluate the limit Substitute x = 0: \frac{1}{0-1} = -1.

Explanation

1. Simplify the expression<br /> Factor the denominator: $x^2 - x = x(x - 1)$. The expression becomes $\frac{x}{x(x-1)}$.<br />2. Cancel common factors<br /> Cancel $x$ in the numerator and denominator: $\frac{1}{x-1}$.<br />3. Evaluate the limit<br /> Substitute $x = 0$: $\frac{1}{0-1} = -1$.
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