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Use Limit Laws to find the limit. Graph each function before you submit the solution to check if the graph supports your conclusion.
For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve.
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit
Find an equation for the hyperbola with the focus (11,12) and asymptotes 4x-3y=18 and 4x+3y=30. Find the arc length of the curve given by x = sin t - cos t, y = sin t + cos t, pi/1
A rectangular study plot is to be enclosed by 625 m of fencing. What are the dimensions of the study plot that will have the largest area?
If the rope is pulled in at a rate of 1.4 m/s, how fast is the boat approaching the dock when it is 10 m from the dock?
If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.
You are experimenting with designs for a fruit bowl with a square base. The general idea is to attach congruent regular polygons to the sides of the base and "fold them up" until the closest edges of adjacent polygons meet.
A plane flying into a headwind travels 216 miles in 2 hours and 42 minutes. The plane does the return flight in 2 hours. Find the speed of the plane and of the wind.
Find correct to four decimal places the length of the curve of intersection of the cylinder 4x2+y2=4 and the plane x+y+z=2
Sketch the Graph of y = cosx in the range -Pi
Rewrite the expression in terms of the first power of the cosine. Use a graphing utility to graph both expressions to verify that both forms
An airplane is flying in still air with an airspeed of 475 miles per hour. If it is climbing at an angle of 25°, find the rate at which it is gaining altitude. (Round answer to four decimal places.)
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