lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 .
(a) On what open intervals contained in 0
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What happened to the European population in the High
ean population in the High Middle Ages?
The number of people almost doubles from 38 million to 74 million people.
List two reasons for the change in population during this time.
Conditions in Europe were more settled and peaceful after the invasions of the early Middle Ages had stopped. Food productions increased because a change in climates improved growing conditions.
What two inventions for the horse made it possible to plow faster?
A new horse collar and the use of the horseshoe.
Define the term manor.
A manor was an agricultural estate run by a lord and worked by peasants.
What three ways did serfs pay rent to their lords?
By giving the lords a share of every product they raised, paying for the use of common pasture lands and turning over a part of the can't from ponds and streams.
Name the three great events celebrated by feasts within the Christian faith.
Christmas (celebrating the birth of Christ), Easter (celebrating the resurrection of Christ), and Pentecost (celebrating the descent of the Holy Spirit on Christ's disciples 50 days after His resurrection).
What two features changed the economic foundation of Europe?
A revival of trade and an associated growth of towns and cities.
For what two reasons did merchants build a settlement rear a castle?
Because it was located along a trade route and because the lords of the castle would offer protection.
By 1100, What four rights were townspeople getting from local lords?
The right to buy and sell property, freedom from military service to the lord, a law guaranteeing the freedom of the townspeople, and the right for an escaped serf to become a free person after living a year and a day in the town.
Describe the environment of medieval cities.
The cities were dirty and smelled from animal and human waste. Air was polluted from wood fires. Water was polluted as well.
What three steps did a person complete to become a master in a build?
He first became an apprentice to a master craftsperson. After 5-7 years he became a journeyman and worked for wages. Upon completing a masterpiece which was judged, he/she could be declared a master and join a guild.