Calculus Examples

$\frac{lim_{x \to 4} (x) (x - 4)}{3 x^{2} - 8 x - 16} + 4$

Step 1

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

$\frac{lim_{x \to 4} x \cdot lim_{x \to 4} x - 4}{3 x^{2} - 8 x - 16} + 4$

Step 2

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

$\frac{lim_{x \to 4} x \cdot (lim_{x \to 4} x - lim_{x \to 4} 4)}{3 x^{2} - 8 x - 16} + 4$

Step 3

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

$\frac{lim_{x \to 4} x \cdot (lim_{x \to 4} x - 1 \cdot 4)}{3 x^{2} - 8 x - 16} + 4$

Step 4

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

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Step 4.1

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

$\frac{4 \cdot (lim_{x \to 4} x - 1 \cdot 4)}{3 x^{2} - 8 x - 16} + 4$

Step 4.2

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

$\frac{4 \cdot (4 - 1 \cdot 4)}{3 x^{2} - 8 x - 16} + 4$

Step 5

Simplify the answer.

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Step 5.1

Multiply $- 1$ by $4$ .

$\frac{4 \cdot (4 - 4)}{3 x^{2} - 8 x - 16} + 4$

Step 5.2

Subtract $4$ from $4$ .

$\frac{4 \cdot 0}{3 x^{2} - 8 x - 16} + 4$

Step 5.3

Multiply $4$ by $0$ .

$\frac{0}{3 x^{2} - 8 x - 16} + 4$

Step 5.4

Combine the opposite terms in $\frac{0}{3 x^{2} - 8 x - 16} + 4$ .

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Step 5.4.1

Divide $0$ by $3 x^{2} - 8 x - 16$ .

$0 + 4$

Step 5.4.2

Add $0$ and $4$ .

$4$