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

What is the value of lim(x → 2) (x⁵ − 32)/(x − 2)?

The limit is 80. Since 32 equals 2⁵, the expression matches the standard form (xⁿ − aⁿ)/(x − a) with n = 5 and a = 2, whose limit is n times a raised to n − 1, giving 5 × 16 = 80.

  1. A32
  2. B40
  3. C80Correct
  4. D10

Explanation

Use lim(x → a) (xⁿ − aⁿ)/(x − a) = n·aⁿ⁻¹. Here n = 5 and a = 2, so the limit is 5 × 2⁴ = 5 × 16 = 80. Option 40 results from using 5 × 2³ (wrong power), and 32 is simply the constant 2⁵.

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