
please rate the answer if you like it and mention in comment if you have any doubt
44. Show that the integral dt in Example 28.11 21/RC has the value RC. We were...
1. (a) Find L4 and R4 for the integral
1 (x sin x/2) dx
Show the setup and round the answer to threedecimal places.
(b) Find M4 for the integral
1 (x sin x/2) dx . Show the setup and round the answer to four
decimal places.
Sketch the approximating rectangles on the graph.
(c) Compare the estimates with the actual value
1 (x sin x/2) dx
10.243 . Which estimate is the most accurate?
(d) Express the integral from...
Find the solution to the given systems
(a) X'=X
X(0)=
(b) dx/dt=5x+y dy/dt=-2x+3y
We were unable to transcribe this imageWe were unable to transcribe this image
Let
be an arbitrary function and A
X.
i) Show that A
ii) Give an example to show that in general A =
.
iii) Show that, if
is injective, then A =
iv) Show that, if X and Y are modules;
is a homomorphism of modules and A is a submodule of X such that
ker,
then we also have A =
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...
let
,
1)Find the initial value problem
2)Find the integral equation.
We were unable to transcribe this imageuec2[0, 1], gec[0, 1], ze(0, 1)
Suppose that
is nonempty and bounded above. Then
has a supremum.
Note: Show that there is a least element
such that
is an upper bound for
. if
is not a least upper bound for
, show there is at least
such that
is an upper bound for
. Proceed in this way to find the supremum.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image21 We were unable to...
A scalar function f :
which is never zero has the properties
and
Evaluate the integral
where
is the surface of the unit sphere
and
means the directional derivative of f in the direction of the
outward pointing unit normal on
.
R? → R We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...
COMPLEX ANALYSIS:
Solve the integral
where
and
.
Please use JORDAN'S LEMMA and show all of your work.
Thank you!
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let
and define
by .
(a) Show is one-to-one
(b) What is the formula for
We were unable to transcribe this imageWe were unable to transcribe this image5r We were unable to transcribe this imageWe were unable to transcribe this image
Use the transformation
and
to evaluate the integral
where
is the region bounded on the
by the ellipse
Let S be the image of R under
T on the .
Sketch regions
R and S. Set up the integral as
an iterated integral of a function
over region S. Use technology to evaluate the
integral. Give the exact answer.
We were unable to transcribe this imageWe were unable to transcribe this imageR xdA We were unable to transcribe this imageWe were...
Evaluate each integral using the definition of the definite
integral with right endpoints and taking the limit. (Note: You need
to write out the Riemann sum and use the summation formulas.)
(a)
0 (x^2+2x-5) dx
x+b-a/n=
xi=a+Ix=
(b)
1 x^3 dx
x=b-a/n=
xi=a+Ix=
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image