1.10 G: Differentiation

The intensity of light $I\,$ at a distance $w\,$ from a source is modeled by the equation

e^{4w} \sec 2w, \quad -\frac{\pi}{4} < w < \frac{\pi}{4}

(a) Find $I^{'} (w)$ . (b) Determine the $w$ -coordinate of the stationary point for the light intensity curve.

[7]

ii.

In a separate experiment, the relationship between a signal $s\,$ and a phase angle $\theta\,$ is given by

\ln(5 \cos \theta), \quad 0 < \theta < \frac{\pi}{2}

Show that

\frac{d\theta}{ds} = -\frac{e^s}{f(s)}

where $f (s)$ is a function of $e^s\,$ to be determined.

[7]

The intensity of light $I\,$ at a distance $w\,$ from a source is modeled by the equation

e^{4w} \sec 2w, \quad -\frac{\pi}{4} < w < \frac{\pi}{4}

(a) Find $I^{'} (w)$ . (b) Determine the $w$ -coordinate of the stationary point for the light intensity curve.

[7]

In a separate experiment, the relationship between a signal $s\,$ and a phase angle $\theta\,$ is given by

\ln(5 \cos \theta), \quad 0 < \theta < \frac{\pi}{2}

Show that

\frac{d\theta}{ds} = -\frac{e^s}{f(s)}

where $f (s)$ is a function of $e^s\,$ to be determined.

1.10 G: Differentiation Questions