A line segment with endpoints \( ( - 4,1 ) \) and \( ( - 1,4 ) \) is reflected across the line \( y = - x \) . Find the coordinates of the endpoints on the reflected line segment.
A. \( ( - 4 , - 1 ) \) and \( ( - 1 , - 4 ) \)
B. \( ( 4,1 ) \) and \( ( 1,4 ) \)
C. \( ( 1 , - 4 ) \) and \( ( 4 , - 1 ) \)
D. \( ( - 1,4 ) \) and \( ( - 4,1 )\)
(-1,4) and (-4,1)
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. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
