Sketching a Graph In Exercises 35 and 36, sketch a graph of a function f that satisfies the given values. (There are many correct answers.) f ( − 2 ) = 0 f ( 0 ) = 0 lim x → − 2 f ( x ) = 0 lim x → 2 f ( x ) does not exist .
Sketching a Graph In Exercises 35 and 36, sketch a graph of a function f that satisfies the given values. (There are many correct answers.) f ( − 2 ) = 0 f ( 0 ) = 0 lim x → − 2 f ( x ) = 0 lim x → 2 f ( x ) does not exist .
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.
Chapter 2 Solutions
Bundle: Calculus: Early Transcendental Functions, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus, Multi-Term
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