The lateral displacement, xxx mm, of a high-precision vibrating needle is modeled by the equation
x=14cos2(4y)0<y<π8 x = 14 \cos^2(4y) \qquad 0 < y < \frac{\pi}{8} x=14cos2(4y)0<y<8πwhere yyy is the angle of the driving cam in radians.
Show that the rate of change of the cam angle with respect to displacement is given by
dydx=−1ABx−x2 \frac{dy}{dx} = -\frac{1}{A\sqrt{Bx - x^2}} dxdy=−ABx−x21where AAA and BBB are integers to be found.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
