Question

\[ \lim_{x \to 0} \frac{\sqrt{1+x} - \sqrt{1 - x}}{x} \]

• A. 0
• B. 1
• C. -1
• D. $\infty$

Hint:

The continuous X-ray spectrum is due to Bremsstrahlung radiation, not characteristic emission.

Answer 1

The Correct Option is B

This is an indeterminate form of \(\frac{0}{0}\). Apply L'Hôpital's Rule: Differentiate the numerator: \[ \frac{d}{dx}[\sqrt{1+x} - \sqrt{1-x}] = \frac{1}{2\sqrt{1+x}} + \frac{1}{2\sqrt{1-x}} \] Differentiate the denominator: \[ \frac{d}{dx}[x] = 1 \] Now compute the limit: \[ \lim_{x \to 0} \left( \frac{1}{2\sqrt{1+x}} + \frac{1}{2\sqrt{1-x}} \right) = \frac{1}{2} + \frac{1}{2} = 1 \]