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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 197

The horizontal position x x\,x of a piston in a high-precision engine is modelled by the equation

x=18cos⁡2(2θ)0<θ<π4 x = 18 \cos^2(2\theta) \qquad 0 < \theta < \frac{\pi}{4} x=18cos2(2θ)0<θ<4π​

where θ \theta\,θ is the crankshaft angle in radians.

Show that the rate of change of the angle with respect to the position, dθdx\displaystyle \frac{d\theta}{dx}dxdθ​, can be expressed in the form

dθdx=−1ABx−x2 \frac{d\theta}{dx} = -\frac{1}{A\sqrt{Bx - x^2}} dxdθ​=−ABx−x2​1​

where A A\,A and B B\,B are integers to be determined.

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3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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