Calculus Examples

$lim_{x \to 5} (x - 4) (x^{2} + 8)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $5$ .

$lim_{x \to 5} x - 4 \cdot lim_{x \to 5} x^{2} + 8$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$(lim_{x \to 5} x - lim_{x \to 5} 4) \cdot lim_{x \to 5} x^{2} + 8$

Step 3

Evaluate the limit of $4$ which is constant as $x$ approaches $5$ .

$(lim_{x \to 5} x - 1 \cdot 4) \cdot lim_{x \to 5} x^{2} + 8$

Step 4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$(lim_{x \to 5} x - 1 \cdot 4) \cdot (lim_{x \to 5} x^{2} + lim_{x \to 5} 8)$

Step 5

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

$(lim_{x \to 5} x - 1 \cdot 4) \cdot ({(lim_{x \to 5} x)}^{2} + lim_{x \to 5} 8)$

Step 6

Evaluate the limit of $8$ which is constant as $x$ approaches $5$ .

$(lim_{x \to 5} x - 1 \cdot 4) \cdot ({(lim_{x \to 5} x)}^{2} + 8)$

Step 7

Evaluate the limits by plugging in $5$ for all occurrences of $x$ .

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Step 7.1

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$(5 - 1 \cdot 4) \cdot ({(lim_{x \to 5} x)}^{2} + 8)$

Step 7.2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$(5 - 1 \cdot 4) \cdot (5^{2} + 8)$

Step 8

Simplify the answer.

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Step 8.1

Multiply $- 1$ by $4$ .

$(5 - 4) \cdot (5^{2} + 8)$

Step 8.2

Subtract $4$ from $5$ .

$1 \cdot (5^{2} + 8)$

Step 8.3

Multiply $5^{2} + 8$ by $1$ .

$5^{2} + 8$

Step 8.4

Raise $5$ to the power of $2$ .

$25 + 8$

Step 8.5

Add $25$ and $8$ .

$33$