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Question

# If 0<x<y, then limnâ†’âˆž(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 yGiven x,y>0 it is max {x,y}This is obvious for x=y lines then max {x,y} = x = yAlso it is obvious if either is 0.0<x<y(yn+xn)1/ny(1+(xy)n)1/nxy = P.y(1+Pn)1/ntake a fixed s such that 0<s<p.for certain value N, pn≤s for all n≥N whichmeans that 1<(1+pn)1/n≤(1+s)1/nforn≥N& we know that limn→∞(1+s)1/n=1.Becomelimn→∞1n(1+s)=0Hence by using square thermlimn→∞(yn+xn)1/n=ylimn→∞(1+s)1/n=yAns :- y

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