Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Move the term $3 g$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to - 3} f (x) - 1 \cdot 3 g lim_{x \to - 3} x$

Step 4

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

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Step 4.1

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

$2 f (- 3) - 1 \cdot 3 g lim_{x \to - 3} x$

Step 4.2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$2 f (- 3) - 1 \cdot 3 g \cdot - 3$

Step 5

Simplify each term.

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Step 5.1

Multiply $- 1$ by $3$ .

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

Step 5.2

Multiply $- 3$ by $- 3$ .

$2 f (- 3) + 9 g$