Question: "Use the conjugate process limx→0x2+5−5−x2x." - Plainmath

Dottie Parra

Answered question

2020-10-27

Use the conjugate process

lim_{x \to 0} \frac{\sqrt{x^{2} + 5} - \sqrt{5 - x^{2}}}{x} .

Answer & Explanation

cheekabooy

Skilled2020-10-28Added 83 answers

The expression simplifies:

\frac{\sqrt{5} \cdot \sqrt{1 + \frac{x^{2}}{5}} - \sqrt{5} \cdot \sqrt{1 - \frac{x^{2}}{5}}}{x} =

\sqrt{5} \frac{\frac{{(1 + \frac{x^{2}}{5})}^{1}}{2} - \frac{{(1 - \frac{x^{2}}{5})}^{1}}{2}}{x}

\Rightarrow \sqrt{5} \frac{(1 + \frac{x^{2}}{10}) - (1 - \frac{x^{2}}{10})}{x} =

\sqrt{5} \frac{2 \frac{x^{2}}{10}}{x} = \sqrt{5} \frac{x}{5}

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