Question:
The value of
limₓtₒᵢₙfty(fraca₁¹/x+a₂¹/x+⋯+aₙ¹/xn)ⁿx,
aᵢ>0
is
The value of
limₓtₒᵢₙfty(fraca₁¹/x+a₂¹/x+⋯+aₙ¹/xn)ⁿx,
aᵢ>0
is
Show Hint
Limits of the form (1+(k)/(x))ˣ tend to exponentials.
Updated On: Mar 19, 2026
- a₁+a₂+⋯+aₙ
- eᵃ_¹⁺ᵃ_²⁺⋯⁺ᵃ_ⁿ
- (a₁+a₂+⋯+aₙ)/(n)
- a₁a₂⋯ aₙ
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
For large x:
aᵢ¹/x≈ 1+(ln aᵢ)/(x)
Hence,
(1+(sum ln aᵢ)/(nx))ⁿx
→ eˢᵘᵐ lⁿ ᵃ_ⁱ
= a₁a₂⋯ aₙ
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