Calculus Examples

$lim_{x \to 8} \frac{0.001 e^{0.1 x}}{6}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{0.001}{6}$ outside of the limit because it is constant with respect to $x$ .

$\frac{0.001}{6} lim_{x \to 8} e^{0.1 x}$

Step 1.2

Move the limit into the exponent.

$\frac{0.001}{6} e^{lim_{x \to 8} 0.1 x}$

Step 1.3

Move the term $0.1$ outside of the limit because it is constant with respect to $x$ .

$\frac{0.001}{6} e^{0.1 lim_{x \to 8} x}$

Step 2

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

$\frac{0.001}{6} e^{0.1 \cdot 8}$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $0.001$ .

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Step 3.1.1

Cancel the common factor.

$\frac{0.001}{6} e^{0.1 \cdot 8}$

Step 3.1.2

Rewrite the expression.

$\frac{1}{6} \cdot \frac{e^{0.1 \cdot 8}}{1000}$

Step 3.2

Multiply $0.1$ by $8$ .

$\frac{1}{6} \cdot \frac{e^{0.8}}{1000}$

Step 3.3

Multiply $\frac{1}{6}$ by $\frac{e^{0.8}}{1000}$ .

$\frac{e^{0.8}}{6 \cdot 1000}$

Step 3.4

Multiply $6$ by $1000$ .

$\frac{e^{0.8}}{6000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{0.8}}{6000}$

Decimal Form:

$0.00037092 \dots$