Calculus Examples

$lim_{x \to \infty} {(\frac{3}{5})}^{\frac{1}{x}}$

Step 1

Move the limit into the exponent.

${(\frac{3}{5})}^{lim_{x \to \infty} \frac{1}{x}}$

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x}$ approaches $0$ .

${(\frac{3}{5})}^{0}$

Step 3

Simplify the answer.

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Step 3.1

Apply the product rule to $\frac{3}{5}$ .

$\frac{3^{0}}{5^{0}}$

Step 3.2

Anything raised to $0$ is $1$ .

$\frac{1}{5^{0}}$

Step 3.3

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 3.4

Divide $1$ by $1$ .

$1$