Calculus Examples

$lim_{x \to 8} (\frac{8}{10}) \log (8) \cdot \sin (π)$

Step 1

Cancel the common factor of $8$ and $10$ .

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Step 1.1

Factor $2$ out of $8$ .

$lim_{x \to 8} \frac{2 (4)}{10} \log (8) \cdot \sin (π)$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $10$ .

$lim_{x \to 8} \frac{2 \cdot 4}{2 \cdot 5} \log (8) \cdot \sin (π)$

Step 1.2.2

Cancel the common factor.

$lim_{x \to 8} \frac{2 \cdot 4}{2 \cdot 5} \log (8) \cdot \sin (π)$

Step 1.2.3

Rewrite the expression.

$lim_{x \to 8} \frac{4}{5} \log (8) \cdot \sin (π)$

Step 2

Evaluate the limit of $\frac{4}{5} \log (8) \cdot \sin (π)$ which is constant as $x$ approaches $8$ .

$\frac{4}{5} \log (8) \cdot \sin (π)$

Step 3

Simplify the answer.

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Step 3.1

Combine $\frac{4}{5}$ and $\log (8)$ .

$\frac{4 \log (8)}{5} \cdot \sin (π)$

Step 3.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{4 \log (8)}{5} \cdot \sin (0)$

Step 3.3

The exact value of $\sin (0)$ is $0$ .

$\frac{4 \log (8)}{5} \cdot 0$

Step 3.4

Multiply $\frac{4 \log (8)}{5}$ by $0$ .

$0$