Limit of \( \displaystyle \frac{\sqrt{x + 3} - 2}{x - 1} \) as \( x \to 1 \)

Problem 1.243 · medium

1. \[ \lim_{x \to 1^+}\left(\frac{\sqrt{x + 3} - 2}{x - 1}\right) \]
   limit algebraState the limit with the specified direction. Multiply the numerator and denominator by the conjugate.✓ Proved
2. \[ = \lim_{x \to 1^+} \frac{1}{\sqrt{x + 3} + 2} \]
   simplify simplify cancelSimplify the numerator. Combine terms in the numerator. Cancel the common factor (x - 1).✓ Proved
3. \[ = \lim_{x \to 1^+} \frac{1}{4} \]
   limitEvaluate the limit by substituting x = 1.✓ Proved
4. \[ = \frac{1}{4} \]
   simplify simplifySimplify the denominator. Final result.✓ Proved