Calculus Examples

$\frac{lim_{x \to - 3} x^{2} - x - 12}{x + 3}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 3$ .

$\frac{lim_{x \to - 3} x^{2} - lim_{x \to - 3} x - lim_{x \to - 3} 12}{x + 3}$

Step 2

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

$\frac{{(lim_{x \to - 3} x)}^{2} - lim_{x \to - 3} x - lim_{x \to - 3} 12}{x + 3}$

Step 3

Evaluate the limit of $12$ which is constant as $x$ approaches $- 3$ .

$\frac{{(lim_{x \to - 3} x)}^{2} - lim_{x \to - 3} x - 1 \cdot 12}{x + 3}$

Step 4

Evaluate the limits by plugging in $- 3$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$\frac{{(- 3)}^{2} - lim_{x \to - 3} x - 1 \cdot 12}{x + 3}$

Step 4.2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$\frac{{(- 3)}^{2} + 3 - 1 \cdot 12}{x + 3}$

Step 5

Simplify the answer.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 3$ to the power of $2$ .

$\frac{9 + 3 - 1 \cdot 12}{x + 3}$

Step 5.1.2

Multiply $- 1$ by $12$ .

$\frac{9 + 3 - 12}{x + 3}$

Step 5.1.3

Add $9$ and $3$ .

$\frac{12 - 12}{x + 3}$

Step 5.1.4

Subtract $12$ from $12$ .

$\frac{0}{x + 3}$

Step 5.2

Divide $0$ by $x + 3$ .

$0$