NDA 2020 Maths · Mathematics · Limits · easy

Lim x→3(x^3-27)/(x^2-9) is equal to

Single correct option

\displaystyle\lim_{x\to3}\dfrac{x^3-27}{x^2-9}

is equal to

Show answer and solution

Answer: (B) $\dfrac92$

Factor:

x^3-27=(x-3)(x^2+3x+9)

and

x^2-9=(x-3)(x+3)

. After cancelling

x-3

the limit is

\dfrac{9+9+9}{6}=\dfrac{27}{6}=\dfrac92

. By L'Hospital's rule the same value is

\dfrac{3x^2}{2x}

x=3

, which is

\dfrac{27}{6}

. The value

\dfrac{27}{2}

is the numerator's derivative at

3

divided by

2

in error, and

9

3x^2/(x)

miscomputed.

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake