f(x) = [x], the greatest integer less then or equal to x and k is an integer. Then, limx→kf(x)=___
A
k
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B
k - 1
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C
k + 1
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D
does not exist
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Solution
The correct option is D does not exist L.H.L = limx→k−f(x)=limh→0f(k−h)=limh→0[k−h]=k−1 R.H.L = limx→k+f(x)=limh→0f(k+h)=limh→0[k+h]=k L.H.L ≠ R.H.L. The limit does not exist for integer values of k.