Calculus Examples

$lim_{k \to 8} \frac{2 k}{k^{2}}$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $k$ and $k^{2}$ .

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Step 1.1.1

Factor $k$ out of $2 k$ .

$lim_{k \to 8} \frac{k \cdot 2}{k^{2}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $k$ out of $k^{2}$ .

$lim_{k \to 8} \frac{k \cdot 2}{k \cdot k}$

Step 1.1.2.2

Cancel the common factor.

$lim_{k \to 8} \frac{k \cdot 2}{k \cdot k}$

Step 1.1.2.3

Rewrite the expression.

$lim_{k \to 8} \frac{2}{k}$

Step 1.2

Move the term $2$ outside of the limit because it is constant with respect to $k$ .

$2 lim_{k \to 8} \frac{1}{k}$

Step 1.3

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

$2 \frac{lim_{k \to 8} 1}{lim_{k \to 8} k}$

Step 1.4

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

$2 \frac{1}{lim_{k \to 8} k}$

Step 2

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

$2 (\frac{1}{8})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $8$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$