1. Given \(f\left( x \right) = 6x + 2\) and \(g\left( x \right) = 10 - 7x\) compute each of the following.
\(\left( {f - g} \right)\left( 2 \right)\)
\(\left( {g - f} \right)\left( 2 \right)\)
\(f\space g\)
\(\displaystyle \left( {\frac{f}{g}} \right)\left( x \right)\)
18
-18
\[f\space g = f\left( x \right)g\left( x \right) = \left( {6x + 2} \right)\left( {10 - 7x} \right) = {{ - 42{x^2} + 46x + 20}}\]\(\left( {\frac{f}{g}} \right)\left( x \right) = \frac{{f\left( x \right)}}{{g\left( x \right)}} = {{\frac{{6x + 2}}{{10 - 7x}}}}\)
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. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
