CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
The value of lim(x → ∞) (1 + 2/x)^x is:
The limit is e squared. The standard result says (1 + a/x)^x tends to e^a as x tends to infinity. With a = 2, the limit is e², not e, because the numerator in the fraction is 2.
- Ae
- Be²Correct
- C2e
- D1
Explanation
Use lim(x → ∞) (1 + a/x)^x = e^a. Here a = 2, so the limit is e². The option e would hold only if the numerator were 1, and 1 wrongly treats the base as tending to 1 so the power as 1.
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