Calculus Examples

$lim_{x \to 0} 4 \sin (x - 3)$

Step 1

Evaluate the limit.

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Step 1.1

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

$4 lim_{x \to 0} \sin (x - 3)$

Step 1.2

Move the limit inside the trig function because sine is continuous.

$4 \sin (lim_{x \to 0} x - 3)$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$4 \sin (lim_{x \to 0} x - lim_{x \to 0} 3)$

Step 1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $0$ .

$4 \sin (lim_{x \to 0} x - 1 \cdot 3)$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$4 \sin (0 - 1 \cdot 3)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 1$ by $3$ .

$4 \sin (0 - 3)$

Step 3.2

Subtract $3$ from $0$ .

$4 \sin (- 3)$

Step 3.3

Evaluate $\sin (- 3)$ .

$4 \cdot - 0.05233595$

Step 3.4

Multiply $4$ by $- 0.05233595$ .

$- 0.20934382$