2. Without using a graphing calculator, identify all of the following equations that graph as straight lines. Explain how you decide.
a. \( y = 3 x \) e. \( y = \frac { 1 } { x } + 3 \)
b. \( y = 2 x ^ { 2 } - 2 \) f. \( y = 7 - x \)
c. \( y = x - 5 \) g. \( y = \frac { 1 } { 2 x + 3 } \)
d. \( y = \sqrt { 2 x + 4 } \) h. \( y = x ^ { 3 }\)
a,c,f
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. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
