Calculus Examples

$\frac{lim_{x \to 0} 12^{x} x}{12^{x} - 1}$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} 12^{x} \cdot lim_{x \to 0} x}{12^{x} - 1}$

Step 2

Move the limit into the exponent.

$\frac{12^{lim_{x \to 0} x} \cdot lim_{x \to 0} x}{12^{x} - 1}$

Step 3

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

Tap for more steps...

Step 3.1

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

$\frac{12^{0} \cdot lim_{x \to 0} x}{12^{x} - 1}$

Step 3.2

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

$\frac{12^{0} \cdot 0}{12^{x} - 1}$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Multiply $12^{0}$ by $0$ .

$\frac{0}{12^{x} - 1}$

Step 4.2

Divide $0$ by $12^{x} - 1$ .

$0$