F x - x - the greatest integer less then or equal to x and k is an integer- Then- lim x - k f x -A- kB- k -1C- k -1D- does not exist

The correct option is D does not existL.H.L = lim_x → k^ f(x) = lim_h → 0 f(k h)= lim_h → 0 [k h] = k 1 R.H.L = lim_x → k^+ f(x) = lim_h → 0 f(k + h)= l ...

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Byju's Answer

Standard XI

Mathematics

Modulus Function

f x =[ x ], t...

Question

f(x) = [x], the greatest integer less then or equal to x and k is an integer. Then, ${lim}_{x \to k} f (x) =$ ___

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k - 1

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k + 1

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does not exist

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Solution

The correct option is D does not exist
L.H.L = ${lim}_{x \to k^{-}} f (x) = {lim}_{h \to 0} f (k - h) = {lim}_{h \to 0} [k - h] = k - 1$
R.H.L = ${lim}_{x \to k^{+}} f (x) = {lim}_{h \to 0} f (k + h) = {lim}_{h \to 0} [k + h] = k$
L.H.L $\neq$ R.H.L. The limit does not exist for integer values of k.

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f(x) = [x], the greatest integer less then or equal to x and k is an integer. Then, limx→kf(x)=___

The correct option is D does not existL.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.

f(x) = [x], the greatest integer less then or equal to x and k is an integer. Then, ${lim}_{x \to k} f (x) =$ ___