Calculus Examples

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

Move the limit inside the trig function because sine is continuous.

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

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{\sin (0)}{2 x^{2} - x}$

Simplify the answer.

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The exact value of $\sin (0)$ is $0$ .

$\frac{0}{2 x^{2} - x}$

Factor $x$ out of $2 x^{2} - x$ .

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Factor $x$ out of $2 x^{2}$ .

$\frac{0}{x (2 x) - x}$

Factor $x$ out of $- x$ .

$\frac{0}{x (2 x) + x \cdot - 1}$

Factor $x$ out of $x (2 x) + x \cdot - 1$ .

$\frac{0}{x (2 x - 1)}$

Divide $0$ by $x (2 x - 1)$ .

$0$