Calculus Examples

$\frac{lim_{x \to 8} x}{\frac{8 x}{\sqrt{9 x^{2} + 6}}}$

Step 1

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

$\frac{8}{\frac{8 x}{\sqrt{9 x^{2} + 6}}}$

Step 2

Simplify the answer.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$8 \frac{\sqrt{9 x^{2} + 6}}{8 x}$

Step 2.2

Cancel the common factor of $8$ .

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Step 2.2.1

Factor $8$ out of $8 x$ .

$8 \frac{\sqrt{9 x^{2} + 6}}{8 (x)}$

Step 2.2.2

Cancel the common factor.

$8 \frac{\sqrt{9 x^{2} + 6}}{8 x}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{9 x^{2} + 6}}{x}$

Step 2.3

Factor $3$ out of $9 x^{2} + 6$ .

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Step 2.3.1

Factor $3$ out of $9 x^{2}$ .

$\frac{\sqrt{3 (3 x^{2}) + 6}}{x}$

Step 2.3.2

Factor $3$ out of $6$ .

$\frac{\sqrt{3 (3 x^{2}) + 3 (2)}}{x}$

Step 2.3.3

Factor $3$ out of $3 (3 x^{2}) + 3 (2)$ .

$\frac{\sqrt{3 (3 x^{2} + 2)}}{x}$