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Question

f(x) = [x], the greatest integer less then or equal to x and k is an integer. Then, limxkf(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 = limxkf(x)=limh0f(kh)=limh0[kh]=k1
R.H.L = limxk+f(x)=limh0f(k+h)=limh0[k+h]=k
L.H.L R.H.L. The limit does not exist for integer values of k.

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