Calculus Examples

$lim_{x \to 6} \sqrt{36 - x^{2}}$

Step 1

Change the two-sided limit into a left sided limit.

$lim_{x \to 6^{-}} \sqrt{36 - x^{2}}$

Step 2

Evaluate the limit.

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Step 2.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 6^{-}} 36 - x^{2}}$

Step 2.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $6$ .

$\sqrt{lim_{x \to 6^{-}} 36 - lim_{x \to 6^{-}} x^{2}}$

Step 2.3

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

$\sqrt{36 - lim_{x \to 6^{-}} x^{2}}$

Step 2.4

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\sqrt{36 - {(lim_{x \to 6^{-}} x)}^{2}}$

Step 3

Evaluate the limit of $x$ by plugging in $6$ for $x$ .

$\sqrt{36 - 6^{2}}$

Step 4

Simplify the answer.

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Step 4.1

Raise $6$ to the power of $2$ .

$\sqrt{36 - 1 \cdot 36}$

Step 4.2

Multiply $- 1$ by $36$ .

$\sqrt{36 - 36}$

Step 4.3

Subtract $36$ from $36$ .

$\sqrt{0}$

Step 4.4

Rewrite $0$ as $0^{2}$ .

$\sqrt{0^{2}}$

Step 4.5

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

$0$