21M.1.AHL.TZ1.8

attempt to differentiate numerator and denominator        M1

$\underset{x\to 0}{\lim }\left(\frac{\text{arctan} 2x}{\tan 3x}\right)$

$=\underset{x\to 0}{\lim }\frac{\left(\frac{2}{1+4x^2}\right)}{3 {\text{sec}}^2 3x}$        A1A1

 

Note: A1 for numerator and A1 for denominator. Do not condone absence of limits.

 

attempt to substitute $x=0$         (M1)

$=\frac{2}{3}$        A1

 

Note: Award a maximum of M1A1A0M1A1 for absence of limits.

 

[5 marks]

[N/A]