A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is radians. The distance (in meters) the ball bearing rolls in t seconds is . Determine the value of after one second. Round numerical values in your answer to one decimal place. ​

The range R of a projectile is  where ν0 is the initial velocity in feet per second and θ is the angle of elevation. If ν0 = 2200 feet per second and θ is changed from 12° to 13° use differentials to approximate the change in the range. Round your answer to the nearest integer. ​

Find the point of inflection of the graph of the function on the interval . ​

Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes. ​

Find the open interval(s) on which is increasing or decreasing. ​

A valve on a storage tank is opened for 4 hours to release a chemical in a manufacturing process. The flow rate R (in liters per hour) at time t (in hours) is given by the linear model . Write the linear model in exponential form. ​

Determine the x-coordinate(s) of any relative extrema and inflection points of the function . ​

For the function : ​ (a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. ​ Then use a graphing utility to confirm your results. ​

Identify the open intervals where the function is increasing or decreasing. ​

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is radians. The distance (in meters) the ball bearing rolls in t seconds is . . Determine the speed of the ball bearing after t seconds. ​