Calculus Examples

$lim_{x \to 8} {(\frac{2}{3})}^{x}$

Step 1

Move the limit into the exponent.

${(\frac{2}{3})}^{lim_{x \to 8} x}$

Step 2

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

${(\frac{2}{3})}^{8}$

Step 3

Simplify the answer.

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Step 3.1

Apply the product rule to $\frac{2}{3}$ .

$\frac{2^{8}}{3^{8}}$

Step 3.2

Raise $2$ to the power of $8$ .

$\frac{256}{3^{8}}$

Step 3.3

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

$\frac{256}{6561}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{256}{6561}$

Decimal Form:

$0.03901844 \dots$