Calculus Examples

$lim_{x \to 9} (f (8.9)) \cdot (2 x^{2}) - 9$

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 $x$ approaches $9$ .

$lim_{x \to 9} (f (8.9)) \cdot (2 x^{2}) - lim_{x \to 9} 9$

Step 1.2

Move the term $f (8.9) \cdot 2$ outside of the limit because it is constant with respect to $x$ .

$f (8.9) \cdot 2 lim_{x \to 9} x^{2} - lim_{x \to 9} 9$

Step 1.3

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

$f (8.9) \cdot 2 {(lim_{x \to 9} x)}^{2} - lim_{x \to 9} 9$

Step 1.4

Evaluate the limit of $9$ which is constant as $x$ approaches $9$ .

$f (8.9) \cdot 2 {(lim_{x \to 9} x)}^{2} - 1 \cdot 9$

Step 2

Evaluate the limit of $x$ by plugging in $9$ for $x$ .

$f (8.9) \cdot 2 \cdot 9^{2} - 1 \cdot 9$

Step 3

Simplify each term.

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Step 3.1

Move $2$ to the left of $f (8.9)$ .

$2 \cdot f (8.9) \cdot 9^{2} - 1 \cdot 9$

Step 3.2

Raise $9$ to the power of $2$ .

$2 f (8.9) \cdot 81 - 1 \cdot 9$

Step 3.3

Multiply $81$ by $2$ .

$162 f (8.9) - 1 \cdot 9$

Step 3.4

Multiply $- 1$ by $9$ .

$162 f (8.9) - 9$