Lim x - x1-3-x-12-3-x-12-3- is

The correct option is A 4/3x →∞lim x^1/3[(x+1)^2/3 (x 1)^2/3] Replacing x→1/h =h→0lim(1+h)^2/3 (1 h)^2/3h Using L Hospital =h→0lim2/3(1+h)^ 1/3+2/3(1 h)^ 1/31 ...

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Byju's Answer

Standard XII

Mathematics

Derivative from First Principle

lim x →∞ x1/3...

Question

$lim x \to \infty x^{\frac{1}{3}} [(x + 1)^{\frac{2}{3}} - (x - 1)^{\frac{2}{3}}]$ is

\frac{4}{3}

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\frac{- 1}{3}

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\frac{1}{3}

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\frac{- 2}{3}

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Solution

The correct option is A $\frac{4}{3}$
$lim x \to \infty x^{\frac{1}{3}} [(x + 1)^{\frac{2}{3}} - (x - 1)^{\frac{2}{3}}]$
Replacing $x \to \frac{1}{h}$
$= lim h \to 0 \frac{(1 + h)^{\frac{2}{3}} - (1 - h)^{\frac{2}{3}}}{h}$
Using L-Hospital
$= lim h \to 0 \frac{\frac{2}{3} (1 + h)^{- \frac{1}{3}} + \frac{2}{3} (1 - h)^{- \frac{1}{3}}}{1} = \frac{4}{3}$

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Similar questions

Q. Find the limit

lim x \to \infty

((x + 1)^{\frac{2}{3}} - (x - 1)^{\frac{2}{3}})

Q. Evaluate:

lim x \to 0 ({(x + 1)}^{\frac{2}{3}} - {(x - 1)}^{\frac{2}{3}})

Q. Evaluate the following limits.

lim x \to \infty ⎛ ⎜ ⎝ {(x + 1)}^{\frac{2}{3}} - {(x + 1)}^{\frac{2}{3}} ⎞ ⎟ ⎠

$l i m x \to 0 \frac{(1 + x)^{\frac{1}{3}} - (1 - x)^{\frac{1}{3}}}{x} =$

lim x \to 1 \frac{\sqrt[3]{x^{2}} - 2. \sqrt[3]{x} + 1}{(x - 1)^{2}}

is equal to

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limx→∞x13[(x+1)23−(x−1)23] is

The correct option is A 43limx→∞x13[(x+1)23−(x−1)23] Replacing x→1h =limh→0(1+h)23−(1−h)23h Using L-Hospital =limh→023(1+h)−13+23(1−h)−131=43

$lim x \to \infty x^{\frac{1}{3}} [(x + 1)^{\frac{2}{3}} - (x - 1)^{\frac{2}{3}}]$ is