Calculus Examples

$lim_{x \to 8} \frac{7^{x}}{3^{x}}$

Step 1

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

$\frac{lim_{x \to 8} 7^{x}}{lim_{x \to 8} 3^{x}}$

Step 2

Move the limit into the exponent.

$\frac{7^{lim_{x \to 8} x}}{lim_{x \to 8} 3^{x}}$

Step 3

Move the limit into the exponent.

$\frac{7^{lim_{x \to 8} x}}{3^{lim_{x \to 8} x}}$

Step 4

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

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Step 4.1

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

$\frac{7^{8}}{3^{lim_{x \to 8} x}}$

Step 4.2

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

$\frac{7^{8}}{3^{8}}$

Step 5

Simplify the answer.

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Step 5.1

Raise $7$ to the power of $8$ .

$\frac{5764801}{3^{8}}$

Step 5.2

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

$\frac{5764801}{6561}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5764801}{6561}$

Decimal Form:

$878.64670019 \dots$