# Lim X → 27 ( X 1 / 3 + 3 ) ( X 1 / 3 − 3 ) X − 27 - Mathematics

$\lim_{x \to 27} \frac{\left( x^{1/3} + 3 \right) \left( x^{1/3} - 3 \right)}{x - 27}$

#### Solution

$\lim_{x \to 27} \frac{\left[ x^\frac{1}{3} + 3 \right] \left[ x^\frac{1}{3} - 3 \right]}{x - 27}$
$= \lim_{x \to 27} \left[ \frac{\left( x^\frac{1}{3} + 3 \right) \left( x^\frac{1}{3} - 3 \right)}{\left( x^\frac{1}{3} \right)^3 - 3^3} \right]$
$x \to 27$
$\therefore x^\frac{1}{3} \to 3$
$Let y = x^\frac{1}{3}$
$\lim_{y \to 3} \left[ \frac{\left( y + 3 \right) \left( y - 3 \right)}{y^3 - 3^3} \right]$
$= \frac{\left( 3 + 3 \right)}{3 \times 3^{3 - 1}}$
$= \frac{6}{3 \times 9}$
$= \frac{2}{9}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.5 | Q 7 | Page 33