Calculus Examples

$lim_{x \to 0} \frac{x^{2} \sin (x) + \cos (x) + x - 1}{x^{2} - 2 x}$

Step 1

Since $\frac{x^{2} \cdot - 1 + \cos (x) + x - 1}{x^{2} - 2 x} \leq \frac{x^{2} \sin (x) + \cos (x) + x - 1}{x^{2} - 2 x} \leq \frac{x^{2} \cdot 1 + \cos (x) + x - 1}{x^{2} - 2 x}$ and $lim_{x \to 0} \frac{x^{2} \cdot - 1 + \cos (x) + x - 1}{x^{2} - 2 x} = lim_{x \to 0} \frac{x^{2} \cdot 1 + \cos (x) + x - 1}{x^{2} - 2 x} = - \frac{1}{2}$ , apply the squeeze theorem.

$- \frac{1}{2}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$