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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

What is the value of lim(x → 0) (√(1 + x) − 1)/x?

The limit is 1/2. Multiplying numerator and denominator by √(1 + x) + 1 cancels x and leaves 1/(√(1 + x) + 1). As x approaches 0, the denominator approaches 2, so the limit is one half.

  1. A1
  2. B0
  3. C1/2Correct
  4. D2

Explanation

Rationalise: (√(1 + x) − 1)/x × (√(1 + x) + 1)/(√(1 + x) + 1) = x/[x(√(1 + x) + 1)] = 1/(√(1 + x) + 1). As x → 0 this becomes 1/(1 + 1) = 1/2. The option 2 inverts the result.

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