Calculus Examples

$lim_{x \to 8} \frac{4 n^{2}}{n^{2} + 10000 n}$

Step 1

Evaluate the limit of $\frac{4 n^{2}}{n^{2} + 10000 n}$ which is constant as $x$ approaches $8$ .

$\frac{4 n^{2}}{n^{2} + 10000 n}$

Step 2

Simplify the answer.

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Step 2.1

Factor $n$ out of $n^{2} + 10000 n$ .

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Step 2.1.1

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

$\frac{4 n^{2}}{n \cdot n + 10000 n}$

Step 2.1.2

Factor $n$ out of $10000 n$ .

$\frac{4 n^{2}}{n \cdot n + n \cdot 10000}$

Step 2.1.3

Factor $n$ out of $n \cdot n + n \cdot 10000$ .

$\frac{4 n^{2}}{n (n + 10000)}$

Step 2.2

Cancel the common factor of $n^{2}$ and $n$ .

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Step 2.2.1

Factor $n$ out of $4 n^{2}$ .

$\frac{n (4 n)}{n (n + 10000)}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Cancel the common factor.

$\frac{n (4 n)}{n (n + 10000)}$

Step 2.2.2.2

Rewrite the expression.

$\frac{4 n}{n + 10000}$