Answer:
1. B
2. 2
3. See below
Step-by-step explanation:
1. Check the length of the segments
A. UV < XY (4 < 4) False
B. WY < UW (5 < 8) True
C. VW > WY (5 > 5) False
D. UX > YV (10 > 10) False
2.
Midpoint of AC = 8
midpoint of AB = 6
The length of the segment between those points is 8-6 = 2
3. If D is the mid point of EF means that ED is the half of EF
x cant be negative so D isnt the mid point of EF
Answer:
=
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
y + 2x = 2 ( subtract 2x from both sides )
y = - 2x + 2 ← in slope- intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
= -
= -
=
Answer:
The Fourier series of f(x) converges to 3 at the points x= π+2kπ, where k is an integer.
Step-by-step explanation:
First, recall that the function f(x) is extended 2π periodic to the whole real line, in order to obtain a valid Fourier expansion. Remember that a Fourier series is formed by a sines and cosines, which are 2π-periodic.
So, the 2π-periodic expansion of f(x) is discontinuous at the points π+2kπ, in particular π and -π. Check the attached figure to a better understanding.
Now, the Dirichlet theorem on the convergence of a Fourier series tells us that the series converges to the function at the points of continuity, and at points of discontinuity the sum of the series is
.
Here we understand the notation and
as
and
.
In this particular case
.
For the limit , with
recall that our function is 2π-periodic, so the values of f near π, with x>π are the same when x is near -π and x>-π. Again, check the attached figure. So,
.
Thus,
.
Note: In the attached figure we only have drawn three repetitions of the 2π-periodic extension of , recall that the extension is <em>ad infinitum</em>. Also, the points drawn in the dotted lines are the sum of the series at the points of discontinuity.
