Calculus Examples

$lim_{n \to 8} \frac{1}{n} \cdot (\sin (\frac{n π}{n}))$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $n$ .

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Step 1.1.1

Cancel the common factor.

$lim_{n \to 8} \frac{1}{n} \cdot \sin (\frac{n π}{n})$

Step 1.1.2

Divide $π$ by $1$ .

$lim_{n \to 8} \frac{1}{n} \cdot \sin (π)$

Step 1.2

Move the term $\sin (π)$ outside of the limit because it is constant with respect to $n$ .

$\sin (π) lim_{n \to 8} \frac{1}{n}$

Step 1.3

Split the limit using the Limits Quotient Rule on the limit as $n$ approaches $8$ .

$\sin (π) \frac{lim_{n \to 8} 1}{lim_{n \to 8} n}$

Step 1.4

Evaluate the limit of $1$ which is constant as $n$ approaches $8$ .

$\sin (π) \frac{1}{lim_{n \to 8} n}$

Step 2

Evaluate the limit of $n$ by plugging in $8$ for $n$ .

$\sin (π) \frac{1}{8}$

Step 3

Simplify the answer.

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Step 3.1

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

$\sin (0) \frac{1}{8}$

Step 3.2

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

$0 (\frac{1}{8})$

Step 3.3

Multiply $0$ by $\frac{1}{8}$ .

$0$