Calculus Examples

$lim_{x \to 0} \frac{x^{4}}{\sin (x - x)}$

Step 1

Evaluate the limit.

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Step 1.1

Subtract $x$ from $x$ .

$lim_{x \to 0} \frac{x^{4}}{\sin (0)}$

Step 1.2

Move the term $\frac{1}{\sin (0)}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{\sin (0)} lim_{x \to 0} x^{4}$

Step 1.3

Move the exponent $4$ from $x^{4}$ outside the limit using the Limits Power Rule.

$\frac{1}{\sin (0)} {(lim_{x \to 0} x)}^{4}$

Step 2

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

$\frac{1}{\sin (0)} \cdot 0^{4}$

Step 3

Simplify the answer.

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Step 3.1

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

$\frac{1}{0} \cdot 0^{4}$

Step 3.2

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{1}{0} \cdot 0^{4}$

Step 4

The expression contains a division by $0$ . The expression is undefined.

Undefined