How do you find the limit of (-2x^2+x)/x as x approaches 0?

May 21, 2016

1

Explanation:

If we substitute x = 0 into the function we obtain $\frac{0}{0}$
which is indeterminate.

However, factorising the numerator gives:

$\frac{x \left(- 2 x + 1\right)}{x} = \frac{\cancel{x} \left(- 2 x + 1\right)}{\cancel{x}} = - 2 x + 1$

now ${\lim}_{x \to 0} \left(- 2 x + 1\right) = 0 + 1 = 1$

$\Rightarrow {\lim}_{x \to 0} \frac{- 2 {x}^{2} + x}{x} = 1$