1. Determine the equation of the tangent to the curve defined by ? = ? ? ?^-x that is parallel to the line represented by 3? ? ? ? 9 = 0. (5 points)

2. An object moves along a line so that, at time t, its position is ? = sin ? /3+cos 2? , where s is the displacement in meters. Calculate the object's velocity at ? = ?/4 .

Thinking and Inquiry 3. Use the definition of derivative to evaluate lim- h (5 points) h-0 4. Determine the equation of the tangent to the curve y = 2-*" at the point on the curve where x = 0. Graph the curve and the tangent at this point. (5 points)7. The profit function of a commodity is P(x) = xe-0.5x, where x > 0. Find the maximum value of the function if x is measured in hundreds of units and P is measured in thousands of dollars. (5 points) 8. A particle moves along a line so that, at time t, its position is s(t) = 8 sin 2t. (5 points) a. For what values of t does the particle change direction? b. What is the particle's maximum velocity