l i m x → 0 ( 1 + x ) 1 3 − ( 1 − x ) 1 3 x = Options: A . &nbsp2/3 B . &nbsp1/3 C . &nbsp1 D . &nbsp0

Answer: Option A : A l i m x → 0 ( 1 + x ) 1 3 − ( 1 − x ) 1 3 x = l i m x → 0 ( 1 + x ) 1 3 − ( 1 − x ) 1 3 ( 1 + x ) − ( 1 − x ) .2 = 2. 1 3

limx→0(1+x)13−(1−x)13x=

Question

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

Options:

A . 2/3

B . 1/3

C . 1

D . 0

Answer: Option A
:
A

l i m x \to 0 \frac{(1 + x)^{\frac{1}{3}} - (1 - x)^{\frac{1}{3}}}{x} = l i m x \to 0 \frac{(1 + x)^{\frac{1}{3}} - (1 - x)^{\frac{1}{3}}}{(1 + x) - (1 - x)} .2 = 2. \frac{1}{3}

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