Calculus Examples

$lim_{x \to 8} 2 p r (r + \frac{12}{r^{2}})$

Step 1

Evaluate the limit of $2 p r (r + \frac{12}{r^{2}})$ which is constant as $x$ approaches $8$ .

$2 p r (r + \frac{12}{r^{2}})$

Step 2

Simplify the answer.

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Step 2.1

Apply the distributive property.

$2 p r \cdot r + 2 p r \frac{12}{r^{2}}$

Step 2.2

Multiply $r$ by $r$ by adding the exponents.

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Step 2.2.1

Move $r$ .

$2 p (r \cdot r) + 2 p r \frac{12}{r^{2}}$

Step 2.2.2

Multiply $r$ by $r$ .

$2 p r^{2} + 2 p r \frac{12}{r^{2}}$

$2 p r^{2} + 2 p r \frac{12}{r^{2}}$

Step 2.3

Cancel the common factor of $r$ .

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Step 2.3.1

Factor $r$ out of $2 p r$ .

$2 p r^{2} + r (2 p) \frac{12}{r^{2}}$

Step 2.3.2

Factor $r$ out of $r^{2}$ .

$2 p r^{2} + r (2 p) \frac{12}{r \cdot r}$

Step 2.3.3

Cancel the common factor.

$2 p r^{2} + r (2 p) \frac{12}{r \cdot r}$

Step 2.3.4

Rewrite the expression.

$2 p r^{2} + 2 p \frac{12}{r}$

$2 p r^{2} + 2 p \frac{12}{r}$

Step 2.4

Combine $2$ and $\frac{12}{r}$ .

$2 p r^{2} + p \frac{2 \cdot 12}{r}$

Step 2.5

Multiply $2$ by $12$ .

$2 p r^{2} + p \frac{24}{r}$

Step 2.6

Combine $p$ and $\frac{24}{r}$ .

$2 p r^{2} + \frac{p \cdot 24}{r}$

Step 2.7

Move $24$ to the left of $p$ .

$2 p r^{2} + \frac{24 p}{r}$

$2 p r^{2} + \frac{24 p}{r}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$