Precalculus Examples

$lim_{n \to 8} 5 n^{2} - 15$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $n$ approaches $8$ .

$lim_{n \to 8} 5 n^{2} - lim_{n \to 8} 15$

Step 1.2

Move the term $5$ outside of the limit because it is constant with respect to $n$ .

$5 lim_{n \to 8} n^{2} - lim_{n \to 8} 15$

Step 1.3

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

$5 {(lim_{n \to 8} n)}^{2} - lim_{n \to 8} 15$

Step 1.4

Evaluate the limit of $15$ which is constant as $n$ approaches $8$ .

$5 {(lim_{n \to 8} n)}^{2} - 1 \cdot 15$

Step 2

Evaluate the limit of $n$ by plugging in $8$ for $n$ .

$5 \cdot 8^{2} - 1 \cdot 15$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raise $8$ to the power of $2$ .

$5 \cdot 64 - 1 \cdot 15$

Step 3.1.2

Multiply $5$ by $64$ .

$320 - 1 \cdot 15$

Step 3.1.3

Multiply $- 1$ by $15$ .

$320 - 15$

Step 3.2

Subtract $15$ from $320$ .

$305$