Precalculus Examples

$lim_{x \to 1} x^{2} + 8 x - 2$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} x^{2} + lim_{x \to 1} 8 x - lim_{x \to 1} 2$

Step 2

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

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

Step 3

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

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

Step 4

Evaluate the limit of $2$ which is constant as $x$ approaches $1$ .

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

Step 5

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$1^{2} + 8 lim_{x \to 1} x - 1 \cdot 2$

Step 5.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$1^{2} + 8 \cdot 1 - 1 \cdot 2$

Step 6

Simplify the answer.

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Step 6.1

Simplify each term.

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Step 6.1.1

One to any power is one.

$1 + 8 \cdot 1 - 1 \cdot 2$

Step 6.1.2

Multiply $8$ by $1$ .

$1 + 8 - 1 \cdot 2$

Step 6.1.3

Multiply $- 1$ by $2$ .

$1 + 8 - 2$

Step 6.2

Add $1$ and $8$ .

$9 - 2$

Step 6.3

Subtract $2$ from $9$ .

$7$