EXN.1.AHL.TZ0.6

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

 attempts to apply l’Hôpital’s rule on $\underset{x\to 0}{\lim }\left(\frac{2x \cos \left(x^2\right)}{5 \tan x}\right)$        M1

$=\underset{x\to 0}{\lim }\left(\frac{2 \cos \left(x^2\right)-4x^2 \sin \left(x^2\right)}{5 {\sec }^2 x}\right)$        M1A1A1

 

Note: Award M1 for attempting to use product and chain rule differentiation on the numerator, A1 for a correct numerator and A1 for a correct denominator. The awarding of A1 for the denominator is independent of the M1.

$=\frac{2}{5}$        A1

 

[5 marks]

[N/A]