Calculus Examples

$lim_{x \to 8} \frac{1}{2} \cdot {(\frac{1.6}{e})}^{6 x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{1}{2}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{2} lim_{x \to 8} {(\frac{1.6}{e})}^{6 x}$

Step 1.2

Move the limit into the exponent.

$\frac{1}{2} {(\frac{1.6}{e})}^{lim_{x \to 8} 6 x}$

Step 1.3

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{2} {(\frac{1.6}{e})}^{6 lim_{x \to 8} x}$

Step 2

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

$\frac{1}{2} {(\frac{1.6}{e})}^{6 \cdot 8}$

Step 3

Simplify the answer.

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Step 3.1

Replace $e$ with an approximation.

$\frac{1}{2} {(\frac{1.6}{2.71828182})}^{6 \cdot 8}$

Step 3.2

Divide $1.6$ by $2.71828182$ .

$\frac{1}{2} \cdot {0.5886071}^{6 \cdot 8}$

Step 3.3

Multiply $6$ by $8$ .

$\frac{1}{2} \cdot {0.5886071}^{48}$

Step 3.4

Raise $0.5886071$ to the power of $48$ .

$\frac{1}{2} \cdot 0$

Step 3.5

Combine $\frac{1}{2}$ and $0$ .

$\frac{0}{2}$

Step 3.6

Divide $0$ by $2$ .

$0$