5. Given a piecewise-defined-function
\( f ( x ) = \left\{ \begin{array} { c c } { 3 } & { , - 4 \leq x \leq - 1 } \\ { x - 2 } & { , - 1 < x < 2 } \\ { \frac { 1 } { 2 } x } & { , 2 \leq x < 4 } \end{array} \right.\)
i) Find the domain of \( f \) . Write your answer in interval notation. ii) Evaluate \( f ( - 2 ) + 2 f ( 3 ) - f ( 0 ) \) .
1) domain:\([- 4,4）\)
2) 8
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. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
