First slide

Introduction to limits

Question

$lim_{x \to 1} \frac{1 - x^{- 2 / 3}}{1 - x^{- 1 / 3}}$ is equal

Moderate

A

2
B

1
C

$\frac{2}{3}$
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to 1} \frac{1 - x^{- 2 / 3}}{1 - x^{- 1 / 3}} = lim_{x \to 1} \frac{1^{2} - {(x^{- 1 / 3})}^{2}}{1 - x^{- 1 / 3}} \\ = lim_{x \to 1} \frac{(1 + x^{- 1 / 3}) (1 - x^{- 1 / 3})}{1 - x^{- 1 / 3}} = lim_{x \to 1} 1 + x^{- 1 / 3} = 1 + 1 = 2 \end{array}$

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