Calculus Examples

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

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

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

Step 2

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

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

Step 3

Simplify terms.

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Step 3.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

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

Step 3.2

Simplify the answer.

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Step 3.2.1

Subtract $1$ from $1$ .

$\frac{0}{1 - \sqrt{x}}$

Step 3.2.2

Divide $0$ by $1 - \sqrt{x}$ .

$0$