Calculus Examples

$\frac{lim_{x \to 49} \sqrt{x - 7}}{x - 49}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\frac{\sqrt{lim_{x \to 49} x - 7}}{x - 49}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $49$ .

$\frac{\sqrt{lim_{x \to 49} x - lim_{x \to 49} 7}}{x - 49}$

Step 1.3

Evaluate the limit of $7$ which is constant as $x$ approaches $49$ .

$\frac{\sqrt{lim_{x \to 49} x - 1 \cdot 7}}{x - 49}$

Step 2

Evaluate the limit of $x$ by plugging in $49$ for $x$ .

$\frac{\sqrt{49 - 1 \cdot 7}}{x - 49}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $- 1$ by $7$ .

$\frac{\sqrt{49 - 7}}{x - 49}$

Step 3.2

Subtract $7$ from $49$ .

$\frac{\sqrt{42}}{x - 49}$