# Basic maths-calculus-Q3

+1 vote

Find  $\dpi{100} \large lim_{x\rightarrow \infty}\begin{pmatrix} \frac{a_1^{1/x}+a_2^{1/x}+...+a_n^{1/x}}{n} \end{pmatrix}^{nx}$where all the $\dpi{100} \large a_i's$ are positive

(A). $\dpi{100} \large a_1 + a_2 + a_3 +...+ a_n$

(B). $\dpi{100} \large a_1 a_2 a_3 ... a_n$

(C). 1

(D). None of these

reshown May 24

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 :