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Question

If 0<x<y, then limn(yn+xn)1/n is equal to :

A
e
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B
x
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C
y
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D
None of these
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Solution

The correct option is C y
Given x,y>0 it is max {x,y}
This is obvious for x=y lines then max {x,y} = x = y
Also it is obvious if either is 0.
0<x<y
(yn+xn)1/n
y(1+(xy)n)1/n
xy = P.
y(1+Pn)1/n
take a fixed s such that 0<s<p.
for certain value N, pns for all nN which
means that 1<(1+pn)1/n(1+s)1/nfornN
& we know that
limn(1+s)1/n=1.
Becomelimn1n(1+s)=0
Hence by using square therm
limn(yn+xn)1/n=ylimn(1+s)1/n=y
Ans :- y

1200755_1295894_ans_8e4aafa0ddb34e79a52a3a010fedac89.jpg

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