Calculus Examples

$lim_{x \to 0} \frac{2 (\sqrt{x + c})}{c} - \frac{2 (\sqrt{x})}{c}$

Step 1

Combine fractions using a common denominator.

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Step 1.1

Combine the numerators over the common denominator.

$lim_{x \to 0} \frac{2 (\sqrt{x + c}) - 2 \sqrt{x}}{c}$

Step 1.2

Factor $2$ out of $2 \sqrt{x + c} - 2 \sqrt{x}$ .

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Step 1.2.1

Factor $2$ out of $- 2 \sqrt{x}$ .

$lim_{x \to 0} \frac{2 (\sqrt{x + c}) + 2 (- \sqrt{x})}{c}$

Step 1.2.2

Factor $2$ out of $2 (\sqrt{x + c}) + 2 (- \sqrt{x})$ .

$lim_{x \to 0} \frac{2 (\sqrt{x + c} - \sqrt{x})}{c}$

Step 2

Because there are no values to the left of $0$ in the domain of $\frac{2 (\sqrt{x + c} - \sqrt{x})}{c}$ , the limit does not exist.

$Does not exist$