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In: Advanced Math

1.Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using...

1.Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = sin(x) + 5 0 < x < 2π increasing decreasing

2. Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = x + 2 cos(x), 0 < x < 2π increasing decreasing

3. Consider the following function. f(x) = x + 1 x2 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = relative minimum (x, y) =

4. s(t) = t3 − 5t2 + 3t − 290 (a) Find the velocity function v(t) of the particle at any time t ≥ 0. v(t) = (b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.) t =

5. An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 75 miles from the point and has a speed of 450 miles per hour. The other is 100 miles from the point and has a speed of 600 miles per hour. (a) At what rate is the distance between the planes changing?-------- mph (b) How much time does the controller have to get one of the airplanes on a different flight path? -------h

6. An airplane flies at an altitude of y = 5 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates (in radians per hour) at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°,and θ = 80°. (a) θ = 30° rad/hr (b) θ = 60° rad/hr (c) θ = 80° (Round your answer to two decimal places.) rad/hr

7. The formula for the volume of a cone is given below. Find the rate of change of the volume for each of the radii given below if dr/dt is 8 inches per minute and h = 18r. V = (1/3)πr2h (a) r = 9 in V' = π in3/min (b) r = 30 in V' = π in3/min

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