A boy who is \( 3 \) feet tall can cast a shadow on the ground that is \( 7 \) feet long. How tall is a man who can cast a shadow that is \( 14 \) feet long?
Set up the proportion by doing ratios of height to length of shadow.
\(x / 14 = 7 / 3 \)
\( 7 / 14 = x / 3 \)
\( x / 3 = 14 / 7 \)
\( 3 / x = 14 / 7\)
\(\frac{x}{3} = \frac{14}{7}\)
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. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
