Calculus Examples

$lim_{x \to 8} \frac{4 + 1000 \cdot \sin (1000)}{2 \cdot 1000 - 3}$

Evaluate the limit of $\frac{4 + 1000 \cdot \sin (1000)}{2 \cdot 1000 - 3}$ which is constant as $x$ approaches $8$ .

$\frac{4 + 1000 \cdot \sin (1000)}{2 \cdot 1000 - 3}$

Simplify the answer.

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Simplify the numerator.

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Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\frac{4 + 1000 \cdot \sin (280)}{2 \cdot 1000 - 3}$

Evaluate $\sin (280)$ .

$\frac{4 + 1000 \cdot - 0.98480775}{2 \cdot 1000 - 3}$

Multiply $1000$ by $- 0.98480775$ .

$\frac{4 - 984.80775301}{2 \cdot 1000 - 3}$

Subtract $984.80775301$ from $4$ .

$\frac{- 980.80775301}{2 \cdot 1000 - 3}$

Simplify the denominator.

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Multiply $2$ by $1000$ .

$\frac{- 980.80775301}{2000 - 3}$

Subtract $3$ from $2000$ .

$\frac{- 980.80775301}{1997}$

Divide $- 980.80775301$ by $1997$ .

$- 0.49114058$