Calculus Examples

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

Step 1

Cancel the common factor of ${(3)}^{2} + 3 - 12$ and $3 - 3$ .

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Step 1.1

Factor $3$ out of ${(3)}^{2}$ .

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

Step 1.2

Factor $3$ out of $3$ .

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

Step 1.3

Factor $3$ out of $3 \cdot 3 + 3 (1)$ .

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

Step 1.4

Factor $3$ out of $- 12$ .

$lim_{x \to 3} \frac{3 \cdot (3 + 1) + 3 (- 4)}{3 - 3}$

Step 1.5

Factor $3$ out of $3 \cdot (3 + 1) + 3 (- 4)$ .

$lim_{x \to 3} \frac{3 \cdot (3 + 1 - 4)}{3 - 3}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $3$ out of $3$ .

$lim_{x \to 3} \frac{3 \cdot (3 + 1 - 4)}{3 (1) - 3}$

Step 1.6.2

Factor $3$ out of $- 3$ .

$lim_{x \to 3} \frac{3 \cdot (3 + 1 - 4)}{3 \cdot 1 + 3 \cdot - 1}$

Step 1.6.3

Factor $3$ out of $3 \cdot 1 + 3 \cdot - 1$ .

$lim_{x \to 3} \frac{3 \cdot (3 + 1 - 4)}{3 \cdot (1 - 1)}$

Step 1.6.4

Cancel the common factor.

$lim_{x \to 3} \frac{3 \cdot (3 + 1 - 4)}{3 \cdot (1 - 1)}$

Step 1.6.5

Rewrite the expression.

$lim_{x \to 3} \frac{3 + 1 - 4}{1 - 1}$

Step 2

Evaluate the limit of $\frac{3 + 1 - 4}{1 - 1}$ which is constant as $x$ approaches $3$ .

$\frac{3 + 1 - 4}{1 - 1}$

Step 3

Simplify the answer.

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Step 3.1

Subtract $1$ from $1$ .

$\frac{3 + 1 - 4}{0}$

Step 3.2

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

Undefined

$\frac{3 + 1 - 4}{0}$

Step 4

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

Undefined