Mathematics Pure Math 2,3 9709: DIFFERENTIATION Topical Past Paper Questions

A curve has equation $ y = \frac{\sin 2x}{3 + \cos x} $ for $ 0 < x < \pi $. (a) Express $ \frac{dy}{dx} $ as a simplified fraction in terms of $ \cos x $. [4] (b) Hence, find an equation of the normal to the curve at the point where $ x = \frac{1}{2}\pi $. Give your answer in an…

A curve has equation $ y = \frac{\tan x}{5 + 2 \sin x} $. **(a)** Express $ \frac{\text{d}y}{\text{d}x} $ as a simplified fraction in terms of $ \sin x $. [4] **(b)** Show that the curve has no stationary points. [2]

The diagram shows the curve $ y = 2\sin x\sqrt{2 + \cos x} $, for $ 0 \leq x \leq 2\pi $, and its minimum point M, where x = a. (a) Find the value of $a$ correct to 2 decimal places. 10^{6} (b) Use the substitution $u=2+\cos x$ to find the exact area of the shaded region $R$. [6]…