Mathematics, high school, exercises, functions, equations, sequences, derivatives, homework, studies
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Abstract
A collection of mathematics exercises and solutions covering functions, equations, sequences, and derivatives for high school students.
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[...] We therefore have . In January 2024, we are at months. On counts then subscribers. From one month to another, we multiply by . The growth rate in percentage is therefore of . Using a spreadsheet, or a calculator, we obtain the following values after each iteration of the algorithm: [...]
[...] The solution of the equation in the interval so it is . Part B so . For all . On the following table of variations: Signes de Variations de Part C On a , et continue on the interval . So by the intermediate value theorem, there exists a real such as . Then we have the following table of signs: Variations of Signes de Knowing that , then the previous table corresponds to the table of signs of . [...]
[...] In fact, we have the following rule: . True . Exercice 2 - Calcul of derivatives , so , so , so , so . Exercise 3 - Solving an equation Let the equation be . One can write it in the following form: . On pose , then we have . so we have two solutions: and . As then we have or . The first solution is impossible because for all values of . So we only have , so . [...]
