A micro-robotic probe moves along a path $C\,$ within a high-precision magnetic field. The relationship between its horizontal displacement $x\,$ and its vertical displacement $y\,$ is defined by the equation

3\sec^2 4y, \quad x > 3, \quad 0 < y < \frac{\pi}{8}

Find an expression for $dxdy\dfrac{dx}{dy}$ in terms of $y$ .

Hence show that

\dfrac{dy}{dx} = \frac{p}{qx\sqrt{x-3}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

Find the equation of the normal to the probe's path $C\,$ at the point where $y=π12\displaystyle y = \frac{\pi}{12}$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are exact constants.

3\sec^2 4y, \quad x > 3, \quad 0 < y < \frac{\pi}{8}

Find an expression for $dxdy\dfrac{dx}{dy}$ in terms of $y$ .

Hence show that

\dfrac{dy}{dx} = \frac{p}{qx\sqrt{x-3}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

1.7.19 Parametric and implicit differentiation (A-level only)

Question 34

Markscheme

1.7.19 Parametric and implicit differentiation (A-level only)

Question 34

Markscheme

1.7.19 Parametric and implicit differentiation (A-level only)

Question 34

1.7.19 Parametric and implicit differentiation (A-level only) Questions

1.7.19 Parametric and implicit differentiation (A-level only)

Question 34

1.7.19 Parametric and implicit differentiation (A-level only) Questions