Calculus Examples

$lim_{n \to 8} \frac{4 i}{n}$

Step 1

Evaluate the limit.

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Step 1.1

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

$4 i lim_{n \to 8} \frac{1}{n}$

Step 1.2

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

$4 i \frac{lim_{n \to 8} 1}{lim_{n \to 8} n}$

Step 1.3

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

$4 i \frac{1}{lim_{n \to 8} n}$

Step 2

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

$4 i \frac{1}{8}$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $4 i$ .

$4 (i) \frac{1}{8}$

Step 3.1.2

Factor $4$ out of $8$ .

$4 (i) \frac{1}{4 (2)}$

Step 3.1.3

Cancel the common factor.

$4 i \frac{1}{4 \cdot 2}$

Step 3.1.4

Rewrite the expression.

$i \frac{1}{2}$

Step 3.2

Combine $i$ and $\frac{1}{2}$ .

$\frac{i}{2}$