Calculus Examples

$lim_{x \to 8} \frac{\ln (4^{t} + 5^{t})}{\frac{3}{\frac{1}{n}}}$

Step 1

Evaluate the limit of $\frac{\ln (4^{t} + 5^{t})}{\frac{3}{\frac{1}{n}}}$ which is constant as $x$ approaches $8$ .

$\frac{\ln (4^{t} + 5^{t})}{\frac{3}{\frac{1}{n}}}$

Step 2

Simplify the answer.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$\ln (4^{t} + 5^{t}) \frac{\frac{1}{n}}{3}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$\ln (4^{t} + 5^{t}) (\frac{1}{n} \cdot \frac{1}{3})$

Step 2.3

Rewrite using the commutative property of multiplication.

$\frac{1}{3} \ln (4^{t} + 5^{t}) \frac{1}{n}$

Step 2.4

Combine $\frac{1}{3}$ and $\ln (4^{t} + 5^{t})$ .

$\frac{\ln (4^{t} + 5^{t})}{3} \cdot \frac{1}{n}$

Step 2.5

Combine.

$\frac{\ln (4^{t} + 5^{t}) \cdot 1}{3 n}$

Step 2.6

Multiply $\ln (4^{t} + 5^{t})$ by $1$ .

$\frac{\ln (4^{t} + 5^{t})}{3 n}$