The intensity of light I I\,I at a distance w w\,w from a source is modeled by the equation
I(w)=e4wsec2w,−π4<w<π4 I(w) = e^{4w} \sec 2w, \quad -\frac{\pi}{4} < w < \frac{\pi}{4} I(w)=e4wsec2w,−4π<w<4π(a) Find I′(w)I'(w)I′(w). (b) Determine the www-coordinate of the stationary point for the light intensity curve.
In a separate experiment, the relationship between a signal s s\,s and a phase angle θ \theta\,θ is given by
s=ln(5cosθ),0<θ<π2 s = \ln(5 \cos \theta), \quad 0 < \theta < \frac{\pi}{2} s=ln(5cosθ),0<θ<2πShow that
dθds=−esf(s) \frac{d\theta}{ds} = -\frac{e^s}{f(s)} dsdθ=−f(s)eswhere f(s)f(s)f(s) is a function of es e^s\,es to be determined.