For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
Solution Summary: The author explains the function f in the graph to determine the values of the functions.
For Exercises 111-114, use the graph of
y
=
f
x
to answer the following. (See Example 10)
a
. Determine
f
−
2
.
b
. Determine
f
3
.
c
. Find all
x
for which
f
x
=
−
1.
d
. Find all
x
for which
f
x
=
−
4.
e
. Determine the
x
-intercept
s
.
f
. Determine the
y
-intercept
.
g
. Determine the domain of
f
.
h
. Determine the range of
f
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.
Interpreting Graphs of Quadratic Equations (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=BHgewRcuoRM;License: Standard YouTube License, CC-BY
Solve a Trig Equation in Quadratic Form Using the Quadratic Formula (Cosine, 4 Solutions); Author: Mathispower4u;https://www.youtube.com/watch?v=N6jw_i74AVQ;License: Standard YouTube License, CC-BY