📘 MATHEMATICS

1. Stating the problem: Create a table with two columns. The first column contains statements of theorems. The second column contains the reasoning/proof behind each theorem. 2. Ex

1. The problem requests a table of statements and reasons for each theorem. 2. Theorems vary widely across mathematics; each theorem typically has a specific statement (what it ass

1. **Calculer les limites demandées** 1) $$\lim_{x \to 1} \frac{\sqrt{10 + x + 3x}}{x^2 + 4x + 3} = \lim_{x \to 1} \frac{\sqrt{10 + 4x}}{x^2 + 4x + 3} = \frac{\sqrt{10 + 4 \times 1

### EXERCISE 1 1. Calculate the limits:

1. Given the universal set $\mu = \{1, 2, 3, 4, 5, 6\}$, sets $A = \{2, 4, 6\}$ and $B = \{1, 2, 3, 4\}$. Find $A \cup B$ (the union). Step 1: The union of two sets combines all un

1. Problem 1: Given universal set $\xi = X \cup Y \cup Z$, with $n(X)=36$, $n(Y)=26$, $n(\xi)=53$, and $n[Y' \cap (X \cap Z)] = 6$, find $n[Y' \cap Z]$. Step 1: Note that $Y' \cap

1. Let's first define the terms: 2. A **subjective** function is usually called **surjective** in mathematics. It means every element in the output set (codomain) has at least one

1. **Problem 27: Calculate the surface area of a triangular-based pyramid with each edge measuring 10 cm.** - The pyramid is a regular tetrahedron with 4 equilateral triangle faces

1. The problem asks us to describe compensation to add or subtract, give examples to teach Grade 4 learners, illustrate numbers with base 10 blocks, test divisibility, and use a pl

1. Problem 1a asks to express $2(\cos 30^\circ + j \sin 30^\circ)$ in the form $a + jb$. 2. Recall that $\cos 30^\circ = \frac{\sqrt{3}}{2}$ and $\sin 30^\circ = \frac{1}{2}$.

1. Tentukan benar atau salah dari pernyataan tentang pembagian kue bolu yang dipotong menjadi 16 bagian. Rani mengambil 4 potong. - Kue yang diambil Rani adalah $\frac{4}{16} = \fr

1. The problem is to understand what a natural number is. 2. Natural numbers are the set of positive integers starting from 1 and going upwards: $1, 2, 3, 4, 5, \dots$

1. The problem is to understand what rounding off means in mathematics and how to apply it. 2. Rounding off is the process of reducing the digits in a number while keeping its valu

1. **Problem 6a:** Determine the number of significant figures in 0.004560. - Leading zeros are not significant.

1. **Énoncé du problème 1:** Déterminer en extension l'ensemble $A = \{x \in \mathbb{Z} \mid \frac{x^2 - x + 2}{2x + 1} \in \mathbb{Z} \}$. 2. **Analyse:** Par définition, $A$ cont

1. Q1 a) Statement: Solve the equation $m/2 + m/3 + 3 = 2 + m/6$. Multiply both sides by 6 to eliminate denominators.

1. The problem asks about the logarithm of infinity factorial, that is \( \log(\infty!) \). 2. First, note that \( \infty! \) is not defined because factorial is defined only for n

1. The problem is to understand the value of $\log(\infty)$. 2. By definition, $\log(x)$ is the inverse function of the exponential function, so $y = \log(x)$ means $x = e^y$ (assu

1. The problem is to understand the value or meaning of the number 2. 2. The number 2 is an integer that comes after 1 and before 3.

1. Problem: How many pairs of twin primes are there between the integers 1 to 100? 1. Work: The twin prime pairs up to 100 are $ (3,5),(5,7),(11,13),(17,19),(29,31),(41,43),(59,61)

1. The problem asks how many pairs of twin primes exist between 1 and 100. Twin primes are pairs of primes that differ by 2. The pairs are (3,5), (5,7), (11,13), (17,19), (29,31),