A piece of paper has an area of \( 256 cm ^ { 2 } \) . A strip is cut off that is \( \frac { 1 } { 4 } \) the original area. From that strip, another strip is cut off that is \( \frac { 1 } { 4 } \) the area of the first, and so on. Here is a graph and table representing sequence \( k \) , where \( k ( n ) \) is the area in square centimeters of the strip of paper after n cuts. (See question at the bottom in Blue.)
Write an \(n^{th} \)term equation to define sequence \( k ( n )\)
\(k(n)= 256\times (\frac{1}{8} )^{n- 1}\)
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. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
