Calculus Examples

$lim_{k \to 8} \frac{k}{3^{k}}$

Step 1

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

$\frac{lim_{k \to 8} k}{lim_{k \to 8} 3^{k}}$

Step 2

Move the limit into the exponent.

$\frac{lim_{k \to 8} k}{3^{lim_{k \to 8} k}}$

Step 3

Evaluate the limits by plugging in $8$ for all occurrences of $k$ .

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Step 3.1

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

$\frac{8}{3^{lim_{k \to 8} k}}$

Step 3.2

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

$\frac{8}{3^{8}}$

Step 4

Raise $3$ to the power of $8$ .

$\frac{8}{6561}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{6561}$

Decimal Form:

$0.00121932 \dots$