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

The value of lim(x → 0) [log(1 + 5x) − log(1 − 5x)]/x, where log is the natural logarithm, is:

The limit is 10. The term log(1 + 5x)/x tends to 5, and log(1 − 5x)/x tends to −5. Subtracting the second from the first gives 5 − (−5) = 10. The two contributions add rather than cancel.

  1. A0
  2. B5
  3. C10Correct
  4. D25

Explanation

Split: log(1 + 5x)/x = 5 × log(1 + 5x)/(5x) → 5. Also −log(1 − 5x)/x = 5 × [−log(1 − 5x)/(−5x)]·(−1)(−1)... directly, log(1 − 5x)/x → −5, so subtracting gives +5. Total = 5 + 5 = 10. Option 5 counts only one of the two terms, and 0 wrongly assumes the terms cancel.

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