4. The concentration of testosterone (in \( ng / dL \) ) in an adult male's blood follows a sinusoidal function with \( 535 ng / dL \) being the maximum concentration and \( 465 ng / dL \) being the minimum. The time it takes to go from maximum to minimum is \( 3 \) hours. Assume there is a maximum at \( t = 0 \) .
i) Determine the equation that models it using \( \cos ( t ) \) .
ii) Graph the concentration of testosterone versus time. Make sure you label your graphs correctly for full marks.
If \( y = f ( g ( h ( x ) ) ) , \) then the derivative \( y ^ { \prime } \) is given by which for
a) \( f ^ { \prime } ( g ( h ( x ) ) \)
b) \( f ^ { \prime } ( g ( h ( x ) ) h ^ { \prime } ( x ) \)
c) None of these
d) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) \)
e) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) h ^ { \prime } ( x )\)
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
