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Question

Let f(x)=[x[x]],g(x)=[x[1x]] and h(x)=[[x]x],, then limx2f(x)+limx12+g(x)+limx2+h(x)=

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 1
Given that
f(x)=[x[x]]

limx2[x]=1

limx2f(x)=limx2[x1]=limx2[x]=1

Therefore, limx2f(x)=1

Given that
g(x)=[x[1x]]

limx12+[1x]=1

limx12+g(x)=limx12+[x×1]=limx12+[x]=0

Therefore, limx12+g(x)=0

Given that
h(x)=[[x]x]

limx2+[x]=2

limx2+h(x)=limx2+[2x]=0

Therefore, limx2+h(x)=0

limx2f(x) + limx12+g(x) + limx2+h(x)=1+0+0

limx2f(x) + limx12+g(x) + limx2+h(x)=1

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