Calculus Examples

$\frac{lim_{x \to 0} 12 x^{2}}{x} - \frac{13^{x}}{x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$\frac{12 lim_{x \to 0} x^{2}}{x} - \frac{13^{x}}{x}$

Step 1.2

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\frac{12 {(lim_{x \to 0} x)}^{2}}{x} - \frac{13^{x}}{x}$

Step 2

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

$\frac{12 \cdot 0^{2}}{x} - \frac{13^{x}}{x}$

Step 3

Simplify the answer.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{12 \cdot 0^{2} - 13^{x}}{x}$

Step 3.2

Simplify each term.

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Step 3.2.1

Raising $0$ to any positive power yields $0$ .

$\frac{12 \cdot 0 - 13^{x}}{x}$

Step 3.2.2

Multiply $12$ by $0$ .

$\frac{0 - 13^{x}}{x}$

Step 3.3

Subtract $13^{x}$ from $0$ .

$\frac{- 13^{x}}{x}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{13^{x}}{x}$