If [x] is the greatest integer function,then | vedclass

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(C) Given that $[x]$ is the greatest integer function.We need to evaluate the limit: $\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{

Vedclass · Accepted Answer

$\frac{8}{3}$

Vedclass · Answer

(C) Given that $[x]$ is the greatest integer function.We need to evaluate the limit: $\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)$.Let $x = 2 + h$,where $h \rightarrow 0^{+}$.As $x \rightarrow 2^{+}$,we have $2 Also,for $2 Since $\frac{2}{3} Substituting these values into the limit:$L = \lim _{h}$ ${\rightarrow 0^{+}}\left(\frac{[2+h]^3}{3}-\left[\frac{2+h}{3}\right]^3\right) = \frac{2^3}{3} - 0^3 = \frac{8}{3}$.

If $[x]$ is the greatest integer function,then $\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)=$

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