Calculus Examples

$lim_{x \to 8} 2 f (x) - 12 h (x)$

Step 1

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

$lim_{x \to 8} 2 f (x) - lim_{x \to 8} 12 h (x)$

Step 2

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to 8} f (x) - lim_{x \to 8} 12 h (x)$

Step 3

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to 8} f (x) - 12 lim_{x \to 8} h (x)$

Step 4

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $f (x)$ by plugging in $8$ for $x$ .

$2 f (8) - 12 lim_{x \to 8} h (x)$

Step 4.2

Evaluate the limit of $h (x)$ by plugging in $8$ for $x$ .

$2 f (8) - 12 h (8)$

Step 5

Subtract $12 h (8)$ from $2 f (8)$ .

$- 10 f (8)$