For Exercises 35-38, a graph of data is given. From visual inspection, which model would best fit the data? Choose from y = m x + b linear y = a b x exponential y = a + b ln x logarithmic y = c 1 + a e − b x logistic
For Exercises 35-38, a graph of data is given. From visual inspection, which model would best fit the data? Choose from y = m x + b linear y = a b x exponential y = a + b ln x logarithmic y = c 1 + a e − b x logistic
Solution Summary: The author determines the best fit model for the given data by using virtual inspection. The graph is a graph of an exponential function.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
University Calculus: Early Transcendentals (4th Edition)
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