111st one turns out to be x2....
Use n>[n]>n-1.
Q1
lim [x2]+[(2x)2]+....[(nx)2]/n
n→∞
Q2 check continuity of f(x) on [1,3]
f(x)=[x2+1]
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4 Answers
1Q.2) easy one.check the continuity at x=1 and x=3.
for x=1, f(1)=2, f(1+)=2
and at x=3, f(3)=10, f(3-)=10
thus its continuous
3The [x] is discontinous at all integer pts. so we have to check where [x2+1] attains integer values for example x2+1=3 at x=±√2 which is in the given interval so there will be a discontinuity at +√2 and we have to do the same for other integers from 3 to 10.