1. Find the derivative of the curve given by the equation: \( 2 ( x - y ) = 3 + \sin y \)
2. There is a point on the curve from #1 between \( - \frac { \pi } { 2 } < y \leq \frac { \pi } { 2 } \) at which the line tangent to the curve has as a slope of 1. Find the coordinates of that point.
\(\frac{1}{2}\cos y+ 1\\(2+ \frac{\pi}{2},0 )\)
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
