Question

Demonstrate (by use of examples) that approximations by high order interpolating polynomials are unstable.

Answer #1

Interpolating polynomials of higher degree tend to be very oscillatory and peaked, especially near the endpoints of the interval.

which can be proved by Runge's phenomenon,

For the case of the Runge function, interpolated at equidistant points, each of the two multipliers in the upper bound for the approximation error grows to infinity with n. Although often used to explain the Runge phenomenon, the fact that the upper bound of the error goes to infinity does not necessarily imply, of course, that the error itself also diverges with n.

Use zero to third order approximations, respectively to
determine f(x) = (4x - 6)3
using base point xi = 2 by Taylor series
expansion. Approximate f(4) and compute true percent
relative error |εt| for each approximation.

An unstable particle produced in a high-energy collision is
measured to have an energy of 483 MeV and an uncertainty in the
energy of 140.78 keV. Use the Heisenberg uncertainty principle to
estimate the lifetime of this particle.

How do MNCs use the spot market in order to hedge? Please
provide examples and an in depth explanation.

A high school chemistry student wishes to demonstrate how water
can be separated into hydrogen and oxygen by electrolysis. She
knows that the reaction will proceed more rapidly if an electrolyte
is added to the water, and has 2.00 M solutions of these reagents
available: H2SO4, HCl, NaCl, Na2SO4, Na2CO3, and CaCO3. which one
would you use?

Demonstrate your understanding of copyright violation, fair use
and ways to be a good digital citizen in today's society by writing
a brief essay (150 to 200 words) on how pirating copyrighted
content is unlawful. Make sure you use definitions of copyright,
fair use and trademarking in your reasoning. Explain why being a
good digital citizen is important and give five examples of how to
be a good digital citizen.

If we use grlex order with x > y > z, is {x 4 y2 − z5, x 3
y3 − 1, x 2 y4 − 2z} a Groebner basis for the ideal generated by
these polynomials? Why or why not?

1) Choose a health condition (DO NOT USE EXAMPLES ex: high blood
pressure, diabetes, etc.).
2) You are a healthcare professional and need to explain
information about the health condition to a patient who has it.
Explain what it is, lifestyle changes, medications needed, etc. Be
specific. Remember to explain the information as if you are
communicating with a patient.

Q: Provide three distinct examples of groups of order 8.
I will give a thumbs up. Thank you. Please try to use group Z if
possible.

This is a special order problem that also requires that you use
the high low method to estimate some cost function parameters, so
you may want to review the high-low method lectures in Module 1. As
with almost all of the analyses that we have done, determining
variable and fixed costs, and knowing what to do with them, is
critical. ______________________________________________________
Huang Automotive is presently operating at 75% of capacity. The
company recently received an offer from a Korean truck...

This is a special order problem that also requires that
you use the high low method to estimate some cost function
parameters, so you may want to review the high-low method lectures
in Module 1. As with almost all of the analyses that we have done,
determining variable and fixed costs, and knowing what to do with
them, is critical.
______________________________________________________
Huang Automotive is presently operating at 75% of capacity. The
company recently received an offer from a Korean truck...

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