Calculus Examples

$\frac{lim_{x \to 2} 1 - \sqrt{x + 1}}{x - 2}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2} 1 - lim_{x \to 2} \sqrt{x + 1}}{x - 2}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$\frac{1 - lim_{x \to 2} \sqrt{x + 1}}{x - 2}$

Step 1.3

Move the limit under the radical sign.

$\frac{1 - \sqrt{lim_{x \to 2} x + 1}}{x - 2}$

Step 1.4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\frac{1 - \sqrt{lim_{x \to 2} x + lim_{x \to 2} 1}}{x - 2}$

Step 1.5

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$\frac{1 - \sqrt{lim_{x \to 2} x + 1}}{x - 2}$

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\frac{1 - \sqrt{2 + 1}}{x - 2}$

Step 3

Add $2$ and $1$ .

$\frac{1 - \sqrt{3}}{x - 2}$