(i) The curve CCC has equation y=g(x)y = \text{g}(x)y=g(x) where
g(x)=e2xsec3x,−π6<x<π6 \text{g}(x) = \text{e}^{2x} \sec 3x, \quad -\frac{\pi}{6} < x < \frac{\pi}{6} g(x)=e2xsec3x,−6π<x<6πFind g′(x)\text{g}'(x)g′(x).
Hence find the xxx-coordinate of the stationary point of CCC.
A different curve has equation
x=ln(cosy),0<y<π2 x = \ln(\cos y), \quad 0 < y < \frac{\pi}{2} x=ln(cosy),0<y<2πShow that
dydx=−exf(x) \frac{\text{d}y}{\text{d}x} = -\frac{\text{e}^x}{\text{f}(x)} dxdy=−f(x)exwhere f(x)\text{f}(x)f(x) is a function of ex\text{e}^xex that should be found.
