The function f is defined parametrically by x = \frac{e^{-t}}{\sqrt{1-t^2}} and y = \sin^{-1} t for -1 < t \le 0.5.
Show that \frac{dy}{dx} = \frac{e^t (1 - t^2)}{t^2 + t - 1}.
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Practise this question\frac{z_3}{z_2} in the form x + iy where x, y \in \mathbb{R}.[3 marks]\arg w = \arg z_3 - [\arg z_1 + \arg z_2], |z_1| = 1 and \arg z_1 = \frac{\pi}{12}, rewrite w = \frac{z_3}{z_1 z_2} in the form…[6 marks]v = x + iy is such that v^2 = 2 + i. Show that x^2 = \frac{2 + \sqrt{5}}{2}.[7 marks]f has no stationary value.[3 marks]More practice: the rest of this paper · more Differentiation II questions · all CAPE Pure Mathematics Unit 2 past papers