Precalculus Examples

$lim_{x \to 2} x^{2} - 9 x$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$lim_{x \to 2} x^{2} - lim_{x \to 2} 9 x$

Step 2

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

${(lim_{x \to 2} x)}^{2} - lim_{x \to 2} 9 x$

Step 3

Move the term $9$ outside of the limit because it is constant with respect to $x$ .

${(lim_{x \to 2} x)}^{2} - 9 lim_{x \to 2} x$

Step 4

Evaluate the limits by plugging in $2$ for all occurrences of $x$ .

Tap for more steps...

Step 4.1

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$2^{2} - 9 lim_{x \to 2} x$

Step 4.2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$2^{2} - 9 \cdot 2$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

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

$4 - 9 \cdot 2$

Step 5.1.2

Multiply $- 9$ by $2$ .

$4 - 18$

Step 5.2

Subtract $18$ from $4$ .

$- 14$