Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

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

Step 2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 \sin (3 \cdot 4^{3})$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Raise $4$ to the power of $3$ .

$4 \sin (3 \cdot 64)$

Step 3.2

Multiply $3$ by $64$ .

$4 \sin (192)$

Step 3.3

Evaluate $\sin (192)$ .

$4 \cdot - 0.20791169$

Step 3.4

Multiply $4$ by $- 0.20791169$ .

$- 0.83164676$