Lecture

Solving Equations with Irrational Parametric Inequalities

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the topic of solving equations and inequalities with irrational parameters, using examples and step-by-step explanations. The slides provide various examples of equations and inequalities to be solved with respect to x, showcasing the process of disjunction of cases and verification of roots.

Official source

Related concepts (32)

Coin

A 'coin' is a small object, usually round and flat, used primarily as a medium of exchange or legal tender. They are standardized in weight, and produced in large quantities at a mint in order to facilitate trade. They are most often issued by a government. Coins often have images, numerals, or text on them. The faces of coins or medals are sometimes called the obverse and the reverse, referring to the front and back sides, respectively. The obverse of a coin is commonly called heads, because it often depicts the head of a prominent person, and the reverse is known as tails.

Coin collecting

Coin collecting is the collecting of coins or other forms of minted legal tender. Coins of interest to collectors often include those that were in circulation for only a brief time, coins with mint errors, and especially beautiful or historically significant pieces. Coin collecting can be differentiated from numismatics, in that the latter is the systematic study of currency as a whole, though the two disciplines are closely interlinked. Many factors determine a coin's value including grade, rarity, and popularity.

Gold coin

A gold coin is a coin that is made mostly or entirely of gold. Most gold coins minted since 1800 are 90–92% gold (22karat), while most of today's gold bullion coins are pure gold, such as the Britannia, Canadian Maple Leaf, and American Buffalo. Alloyed gold coins, like the American Gold Eagle and South African Krugerrand, are typically 91.7% gold by weight, with the remainder being silver and copper. Traditionally (up to about the 1930s), gold coins have been circulation coins, including coin-like bracteates and dinars.

Fair coin

In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin. John Edmund Kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a crown and coated on one side with lead landed heads (wooden side up) 679 times out of 1000.

Coin flipping

Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to choose between two alternatives, heads or tails, sometimes used to resolve a dispute between two parties. It is a form of sortition which inherently has two possible outcomes. The party who calls the side that is facing up when the coin lands wins. Coin flipping was known to the Romans as navia aut caput ("ship or head"), as some coins had a ship on one side and the head of the emperor on the other.

Related lectures (51)

Absolute Values: Equations and Inequalities

Explores absolute values in equations and inequalities, focusing on solving |f(x)| = g(x).

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Linear Algebra: Identical Applications

Explores identical applications in linear algebra, discussing their representation and implications through examples and equation solving.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Quadratic Equation: Programming Solutions