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Question
limx→1(1−x+[x−1]+[1−x]) is equal to (where [.] denotes greatest integer function)
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Solution
The correct option is C −1
RHL=limh→0f(1+h)=limh→0(1−(1+h)+[1+h−1]+[1−(1+h)])=limh→0(−h+[h]+[−h])=−0+0−1=−1LHL=limh→0f(1−h)=limh→0(1−(1−h)+[1−h−1]+[1−(1−h)])=limh→0(1−1+h+[−h]+[h])=0−1+0=−1∴Limitvalue=−1
RHL=limh→0f(1+h)=limh→0(1−(1+h)+[1+h−1]+[1−(1+h)])=limh→0(−h+[h]+[−h])=−0+0−1=−1LHL=limh→0f(1−h)=limh→0(1−(1−h)+[1−h−1]+[1−(1−h)])=limh→0(1−1+h+[−h]+[h])=0−1+0=−1∴Limitvalue=−1
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