📘 algebra, calculus

1. **Exercice 5 : Déterminer une primitive pour chaque fonction** **Problème :** Trouver une fonction $F$ telle que $F'(x) = f(x)$ pour chaque fonction donnée, en précisant l'inter

1. **Comparer les nombres \(\sqrt{5}\) et \(\sqrt{3}\)** On sait que \(5 > 3\), donc \(\sqrt{5} > \sqrt{3}\).

1. Problem 11(a): Given the cubic equation $$x^3 + px^2 + qx + r = 0$$ with roots $$\alpha, \beta, \gamma$$, form the equation whose roots are $$\alpha\beta, \beta\gamma, \gamma\al

1. Problem: Simplify the rational expression $$\frac{12x^2 - 7x - 10}{3x + 2}$$. 2. Use polynomial division or factorization to simplify.

1. **Matrix Multiplication Problem:** Given matrices

1. **State the problem:** Evaluate each of the given mathematical expressions. 2. **Evaluate each expression step-by-step:**

1. **State the problems:** We have multiple expressions to evaluate or simplify:

1. **Simplifier l'expression** : $$B = \frac{4\sqrt{\sqrt{9} \times \sqrt{27}}}{\sqrt{81}}$$ - Calculons chaque racine : $$\sqrt{9} = 3$$, $$\sqrt{27} = 3\sqrt{3}$$, $$\sqrt{81} =

1. **Problem 1:** Find constants $a$, $b$, and $c$ in the expansion of $(2 + bx)^8 = a + 256x + cx^2$. 2. The binomial expansion formula is $$(p + q)^n = \sum_{k=0}^n \binom{n}{k}

1. The problem involves evaluating and understanding several mathematical expressions: $e^6$, $\log_6(6)$, $\infty$, $\int_1^2 x \, dx$, $\sum_{i=0}^4 i$, $i$, $3!$, $\sqrt{21}$, a

1. **Problem 3.1:** Graph the circle given by $$x^2 + y^2 = 7$$ and determine its domain and range. 2. The equation represents a circle centered at the origin with radius $$r = \sq

1. **Problem 3.1:** Graph the circle given by the equation $$x^2 + y^2 = 7$$ and determine its domain and range. 2. The equation represents a circle centered at the origin with rad

1. The problem is to analyze the function $$f(x)=\frac{e^{5x}}{x^3-1}$$. 2. First, note the function involves an exponential numerator and a cubic denominator.

1. Problem 1: Find the velocity of the end of the spring at $t=1$ s given $s = ae^{-kt} \sin 2\pi ft$ with $a=2$, $k=0.9$, $f=5$. 2. Differentiate $s$ with respect to $t$ to find v