Calculus Examples

$\frac{lim_{x \to 9} 9 - x}{\sqrt{x} - 3}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $9$ .

$\frac{lim_{x \to 9} 9 - lim_{x \to 9} x}{\sqrt{x} - 3}$

Step 2

Evaluate the limit of $9$ which is constant as $x$ approaches $9$ .

$\frac{9 - lim_{x \to 9} x}{\sqrt{x} - 3}$

Step 3

Simplify terms.

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Step 3.1

Evaluate the limit of $x$ by plugging in $9$ for $x$ .

$\frac{9 - 9}{\sqrt{x} - 3}$

Step 3.2

Simplify the answer.

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Step 3.2.1

Subtract $9$ from $9$ .

$\frac{0}{\sqrt{x} - 3}$

Step 3.2.2

Divide $0$ by $\sqrt{x} - 3$ .

$0$