Refer to the graph of y = f x and complete the statements. a . As x → − ∞ f x → _____ . b . As x → − 2 − , f x → _____ . c . As x → − 2 + , f x → _____ . d . As x → ∞ , f x → _____ . e. The graph is increasing over the interval(s) _____ . f. The graph is decreasing over the interval(s) _____ . g. The domain is _____ . h. The range is _____ . i. The vertical asymptote is the line _____ . j. The horizontal asymptote is the line _____ .
Refer to the graph of y = f x and complete the statements. a . As x → − ∞ f x → _____ . b . As x → − 2 − , f x → _____ . c . As x → − 2 + , f x → _____ . d . As x → ∞ , f x → _____ . e. The graph is increasing over the interval(s) _____ . f. The graph is decreasing over the interval(s) _____ . g. The domain is _____ . h. The range is _____ . i. The vertical asymptote is the line _____ . j. The horizontal asymptote is the line _____ .
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.
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.
RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY