Calculus Examples

$lim_{x \to - 3} 4 f (x) - 2$

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 $- 3$ .

$lim_{x \to - 3} 4 f (x) - lim_{x \to - 3} 2$

Step 1.2

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$4 lim_{x \to - 3} f (x) - lim_{x \to - 3} 2$

Step 1.3

Evaluate the limit of $2$ which is constant as $x$ approaches $- 3$ .

$4 lim_{x \to - 3} f (x) - 1 \cdot 2$

Step 2

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

$4 f (- 3) - 1 \cdot 2$

Step 3

Multiply $- 1$ by $2$ .

$4 f (- 3) - 2$