Calculus Examples

$lim_{x \to 3} f (x) - 2 g (x)$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3$ .

$lim_{x \to 3} f (x) - lim_{x \to 3} 2 g (x)$

Step 2

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

$lim_{x \to 3} f (x) - 2 lim_{x \to 3} g (x)$

Step 3

Evaluate the limits by plugging in $3$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $f (x)$ by plugging in $3$ for $x$ .

$f (3) - 2 lim_{x \to 3} g (x)$

Step 3.2

Evaluate the limit of $g (x)$ by plugging in $3$ for $x$ .

$f (3) - 2 g (3)$

Step 4

Subtract $2 g (3)$ from $f (3)$ .

$- f (3)$