Limx - 2-x-3-3 - - x-3 -3 is equal to-where - is GIF

The correct option is B 8/3 lim_x → 2^+{[x]^33 [ x3 ]^3 } =lim _ h→ 0 { [2+h]^ 3 3 [ 2+h 3 #160; ] ^ 3 } = 1 3 × 2^ 3 0= 8 3 ...

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Byju's Answer

Standard XII

Mathematics

Summation by Sigma Method

limx → 2+[x]3...

Question

$lim x \to 2^{+} {\frac{[x]^{3}}{3} - {[\frac{x}{3}]}^{3}}$ is equal to?
(where $[.]$ is GIF)

0

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\frac{64}{27}

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\frac{8}{3}

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none of these

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Solution

The correct option is B $\frac{8}{3}$
$lim x \to 2^{+} {\frac{[x]^{3}}{3} - {[\frac{x}{3}]}^{3}}$

$= lim h \to 0 {\frac{[2 + h]^{3}}{3} - {[\frac{2 + h}{3}]}^{3}}$

$= \frac{1}{3} \times 2^{3} - 0 = \frac{8}{3}$

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limx→2+{[x]33−[x3]3} is equal to?(where [.] is GIF)

The correct option is B 83limx→2+{[x]33−[x3]3}=limh→0{[2+h]33−[2+h3]3}=13×23−0=83

$lim x \to 2^{+} {\frac{[x]^{3}}{3} - {[\frac{x}{3}]}^{3}}$ is equal to?
(where $[.]$ is GIF)

The correct option is B $\frac{8}{3}$
$lim x \to 2^{+} {\frac{[x]^{3}}{3} - {[\frac{x}{3}]}^{3}}$

$= lim h \to 0 {\frac{[2 + h]^{3}}{3} - {[\frac{2 + h}{3}]}^{3}}$

$= \frac{1}{3} \times 2^{3} - 0 = \frac{8}{3}$