Show that
for −1 ≤ x ≤ 1 .
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This is for Calculus 2. Including steps would be wonderful and any help would be nice.

Show that for −1 ≤ x ≤ 1 . This is for Calculus 2. Including steps...
For each
. Find the intersection of and prove.
Please show and explain steps.
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Let X be a banach space such that X= C([a,b]) where - ab+ with the sup
norm. Let x and f X. Show
that the non linear integral equation
u(x) = (sin
u(y) dy + f(x) ) has a solution u X. (the integral is
from a to b).
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Let f(x)=
if
,
if
if
a) What is the fomain of f(x)? Write in interval notation.
b) Determine the y-intercept of the function, if any. Make sure
to justify your answer.
c) Determine the x-intercepts of the function, if any. Justify
your answer.
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Question
If
a) Find the angle between
b) Find a scalar projection and a vector projection of
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Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
sin 0, cos 0
Name the quadrant in which the angle lies
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(6) The sequence of random variable
are independent of each other and they follow the normal
distribution
.
However, the actual value of were not
observed, instead we only observed if each is either
greater than or
equal to 0, or less than 0.
And you can use the fact that there is the inverse function
that is continuous.
Answer the following questions.
Find
the maximum likelihood estimator
of .
When
, show
, where
represents conversion of probability....
Solve the harmonic oscillator motion for initial conditions x(0)
= 0, V(0) = V0 in the case of (a) underdamped
(b) overdamped
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Calculate the work done by the vector field F(x,y)=4xy,
2x2
along a smooth, simple curve from point (3, −1) to point (4, 2)
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Show that a bounded and monotone sequence converges. Here a
sequence
is called monotone, if it is either monotone increasing, that is
for all
or monotone decreasing, in which case
for all
.
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