CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
What is the value of lim(x → ∞) (1 + 3/x)^(2x)?
The limit is e⁶. Rewrite the expression as the square of (1 + 3/x)^x. That inner term tends to e³ as x tends to infinity, so squaring it gives e⁶.
- Ae⁶Correct
- Be⁵
- Ce³
- De²
Explanation
Use lim(x → ∞) (1 + k/x)^x = e^k. Here (1 + 3/x)^(2x) = [(1 + 3/x)^x]². The inner limit is e³, so the result is (e³)² = e⁶. Option e³ ignores the exponent 2, and e⁵ wrongly adds 3 and 2.
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