(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.
825 exam-style questions on OCR (MEI) A Level Maths 1.9 Calculus, covering 1.9.1 Gradient of a curve at a point, 1.9.2 Gradient as limit of chord gradient, 1.9.3 Derivative as gradient of tangent, 1.9.4 Sketch the gradient function, 1.9.5 Differentiate y = kx^n, 1.9.6 Second derivative as rate of change of gradient, 1.9.7 Stationary points: maxima and minima, 1.9.8 Increasing and decreasing functions, 1.9.9 Tangent and normal at a point, 1.9.10 Differentiate e^kx, a^kx and ln x (A-level only), 1.9.11 Differentiate trigonometric functions (A-level only), 1.9.12 Product rule (A-level only), 1.9.13 Quotient rule (A-level only), 1.9.14 Chain rule (A-level only), 1.9.15 Rates of change with the chain rule (A-level only), 1.9.16 Implicit differentiation (A-level only), 1.9.17 Concavity and the second derivative (A-level only), 1.9.18 Points of inflection (A-level only), 1.9.19 Integration as reverse of differentiation, 1.9.20 Integrate kx^n, 1.9.21 Constant of integration, 1.9.22 Indefinite and definite integrals, 1.9.23 Area between a graph and the x-axis, 1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only), 1.9.25 Integration as the limit of a sum (A-level only), 1.9.26 Area between two curves (A-level only), 1.9.27 Integration by substitution (reverse chain rule) (A-level only), 1.9.28 Integration by substitution (other cases) (A-level only), 1.9.29 Integration by parts (A-level only), 1.9.30 Integration using partial fractions (A-level only), 1.9.31 Formulate first order differential equations (A-level only), 1.9.32 Solve first order differential equations (A-level only), and 1.9.33 Interpret solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.