CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
What is the value of lim(x → 0) (2^x − 1)/x?
The limit is the natural logarithm of 2. The standard result says (aˣ − 1)/x tends to log a as x tends to 0, and here a = 2, so the value is log 2, about 0.693, not 1 or 2.
- A1
- B2
- Clog 2 (natural logarithm of 2)Correct
- D1/log 2
Explanation
The standard formula is lim(x → 0) (aˣ − 1)/x = log a (natural log). With a = 2, the limit is log 2, approximately 0.693. Option 1 applies the result for eˣ, and option 2 mistakes the base for the limit.
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