Calculus Examples

$lim_{x \to 36} \frac{1}{\sqrt{x} + 6}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $36$ .

$\frac{lim_{x \to 36} 1}{lim_{x \to 36} \sqrt{x} + 6}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $36$ .

$\frac{1}{lim_{x \to 36} \sqrt{x} + 6}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $36$ .

$\frac{1}{lim_{x \to 36} \sqrt{x} + lim_{x \to 36} 6}$

Step 1.4

Move the limit under the radical sign.

$\frac{1}{\sqrt{lim_{x \to 36} x} + lim_{x \to 36} 6}$

Step 1.5

Evaluate the limit of $6$ which is constant as $x$ approaches $36$ .

$\frac{1}{\sqrt{lim_{x \to 36} x} + 6}$

Step 2

Evaluate the limit of $x$ by plugging in $36$ for $x$ .

$\frac{1}{\sqrt{36} + 6}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $36$ as $6^{2}$ .

$\frac{1}{\sqrt{6^{2}} + 6}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{6 + 6}$

Step 3.3

Add $6$ and $6$ .

$\frac{1}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{12}$

Decimal Form:

$0.08\overline{3}$