a. Graph f x = 2 x . (See Example 1) b. Is f a one-to-one function? c. Write the domain and range of f in interval notation. d. Graph f − 1 on the same coordinate system as f . e. Write the domain and range of f − 1 in interval notation. f. From the graph evaluate f − 1 (1), f − 1 (2), and f − 1 (4).
a. Graph f x = 2 x . (See Example 1) b. Is f a one-to-one function? c. Write the domain and range of f in interval notation. d. Graph f − 1 on the same coordinate system as f . e. Write the domain and range of f − 1 in interval notation. f. From the graph evaluate f − 1 (1), f − 1 (2), and f − 1 (4).
Solution Summary: The author explains that the function f(x)=2x is a one-to-one function.
c. Write the domain and range of f in interval notation.
d. Graph
f
−
1
on the same coordinate system as f.
e. Write the domain and range of
f
−
1
in interval notation.
f. From the graph evaluate
f
−
1
(1),
f
−
1
(2), and
f
−
1
(4).
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
1. Given the vector field F(x, y, z) = -zi, verify the relation
1
VF(0,0,0) lim
+0+ volume inside S
ff F• Nds
S.
where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Let a = (-4, 5, 4) and 6 = (1,0, -1).
Find the angle between the vector
1) The exact angle is cos
2) The approximation in radians is
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY