Basic maths-calculus-Q3

+1 vote

Find  \large lim_{x\rightarrow \infty}\begin{pmatrix} \frac{a_1^{1/x}+a_2^{1/x}+...+a_n^{1/x}}{n} \end{pmatrix}^{nx}where all the \large a_i's are positive

(A). \large a_1 + a_2 + a_3 +...+ a_n

(B). \large a_1 a_2 a_3 ... a_n

(C). 1

(D). None of these

asked May 19 in Basic Maths by gbeditor (44,560 points)
reshown May 24 by gbeditor

1 Answer

0 votes
 
Best answer

by putting x = \infty, we can see that it is in the form 1^{\infty}.

We know that  when 1^{\infty} form is there, then 

 lim (f)^g = e^{lim(f-1).g}    where f \rightarrow 1; g \rightarrow \infty

So, For the given question, answer will be :

https://doubtnut.com/question-answer/evaluate-limnvecooa1-1-x-a2-1-x-a-n1-x-nn-x-28260

 

answered May 27 by deepak-gatebook (112,760 points)
This question falls under easier category or hard category?
This is a simple question in Limits. 1^infinite limit is usually solved like this.
Answer:
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