Precalculus Examples

$\frac{lim_{x \to 4} x^{2} - 3 x - 4}{| x^{2} - 25 | - 9}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$\frac{lim_{x \to 4} x^{2} - lim_{x \to 4} 3 x - lim_{x \to 4} 4}{| x^{2} - 25 | - 9}$

Step 2

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

$\frac{{(lim_{x \to 4} x)}^{2} - lim_{x \to 4} 3 x - lim_{x \to 4} 4}{| x^{2} - 25 | - 9}$

Step 3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\frac{{(lim_{x \to 4} x)}^{2} - 3 lim_{x \to 4} x - lim_{x \to 4} 4}{| x^{2} - 25 | - 9}$

Step 4

Evaluate the limit of $4$ which is constant as $x$ approaches $4$ .

$\frac{{(lim_{x \to 4} x)}^{2} - 3 lim_{x \to 4} x - 1 \cdot 4}{| x^{2} - 25 | - 9}$

Step 5

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$\frac{4^{2} - 3 lim_{x \to 4} x - 1 \cdot 4}{| x^{2} - 25 | - 9}$

Step 5.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$\frac{4^{2} - 3 \cdot 4 - 1 \cdot 4}{| x^{2} - 25 | - 9}$

Step 6

Simplify the answer.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $4$ to the power of $2$ .

$\frac{16 - 3 \cdot 4 - 1 \cdot 4}{| x^{2} - 25 | - 9}$

Step 6.1.2

Multiply $- 3$ by $4$ .

$\frac{16 - 12 - 1 \cdot 4}{| x^{2} - 25 | - 9}$

Step 6.1.3

Multiply $- 1$ by $4$ .

$\frac{16 - 12 - 4}{| x^{2} - 25 | - 9}$

Step 6.1.4

Subtract $12$ from $16$ .

$\frac{4 - 4}{| x^{2} - 25 | - 9}$

Step 6.1.5

Subtract $4$ from $4$ .

$\frac{0}{| x^{2} - 25 | - 9}$

Step 6.2

Divide $0$ by $| x^{2} - 25 | - 9$ .

$0$