Finding the Average Value of a Function In Exercises 51-56, And the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f ( x ) = cos x , [ 0 , π ]
Finding the Average Value of a Function In Exercises 51-56, And the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f ( x ) = cos x , [ 0 , π ]
Solution Summary: The author calculates the average value of a function f(x)=mathrmcosx over the given interval.
Finding the Average Value of a Function In Exercises 51-56, And the average value of the function over the given interval and all values of x in the interval for which the function equals its average value.
Force The force F (in newtons) of a hydraulic cylinder in
a press is proportional to the square of sec x, where x is the
distance (in meters) that the cylinder is extended in its cycle.
The domain of F is [0, 1/3], and F(0) = 500.
(a) Find F as a function of x.
(b) Find the average force exerted by the press over the
interval [0, 1/3].
Describing the closed interval and determining the function values
The range R of the projectile fired from the origin over
horizontal ground is the distance from the origin to the
point of impact. If the projectile is fired with an initial
velocity of
at an angle a with the horizontal, then
R=
2 sin(a) cos (a) where g is the downward
g
acceleration due to gravity.
Using a slingshot, Danny George, of the UK, fired a 3/8-
inch projectile at a speed of 654 feet per second. This
is a Guinness World Record and so we know it took
place here on planet Earth where downward
acceleration due to gravity is g= 32.17
sec?
We want to determine what angle a Danny George
should have used to maximize the range of the
projectile and what the greatest range that can be
achieved is.
Over what closed interval of angles are you trying to
find the maximum range?
Create a table of function values for R that includes the
endpoints of your closed interval and any critical
numbers that are in the closed…
Graphical Reasoning In Exercises69–72, find a, b, and c for the functionf(x) = a sin(bx − c) such that the graph of fmatches the figure.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.