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8 physics teachers in Douala

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8 physics teachers in Douala

Trusted teacher: Digital suites courses I - General A numeric sequence is an application from N to R. • Bounded sequence A sequence (Un) is bounded if there exists a real A such that, for all n, Un ≤ A. We say that A is an upper bound of the series. A sequence (Un) is reduced if there exists a real number B such that, for all n, B ≤ one. One says that B is a lower bound of the sequence. A sequence is said to be bounded if it is both increased and reduced, that is to say if it exists M such that | Un | ≤ M for all n. • Convergent suite The sequence (Un) is convergent towards l ∈ R if: ∀ε> 0 ∃n0 ∈ N ∀n ≥ n0 | un − l | ≤ ε. A sequence which is not convergent is said to be divergent. When it exists, the limit of a sequence is unique. The deletion of a finite number of terms does not modify the nature of the sequence, nor its possible limit. Any convergent sequence is bounded. An unbounded sequence cannot therefore be convergent. • Infinite limits We say that the following (un) diverges Towards + ∞ if: ∀A> 0 ∃n0∈N ∀n ≥ n0 Un≥A Towards −∞ if: ∀A> 0 ∃n0∈N ∀n≤ n0 Un≤A. • Known limitations For k> 1, α> 0, β> 0 II Operations on suites • Algebraic operations If (un) and (vn) converge towards l and l ', then the sequences (un + vn), (λun) and (unvn) respectively converge towards l + l', ll and ll '. If (un) tends to 0 and if (vn) is bounded, then the sequence (unvn) tends to 0. • Order relation If (un) and (vn) are convergent sequences such that we have a ≤ vn for n≥n0, then we have: Attention, no analogous theorem for strict inequalities. • Framing theorem If, from a certain rank, un ≤xn≤ vn and if (un) and (vn) converge towards the same limit l, then the sequence (xn) is convergent towards l. III monotonous suites • Definitions The sequence (un) is increasing if un + 1≥un for all n; decreasing if un + 1≤un for all n; stationary if un + 1 = one for all n. • Convergence Any sequence of increasing and increasing reals converges. Any decreasing and underestimating sequence of reals converges. If a sequence is increasing and not bounded, it diverges towards + ∞. • Adjacent suites The sequences (un) and (vn) are adjacent if: (a) is increasing; (vn) is decreasing; If two sequences are adjacent, they converge and have the same limit. If (un) increasing, (vn) decreasing and un≤vn for all n, then they converge to l1 and l2. It remains to show that l1 = l2 so that they are adjacent. IV Extracted suites • Definition and properties - The sequence (vn) is said to be extracted from the sequence (un) if there exists a map φ of N in N, strictly increasing, such that vn = uφ (n). We also say that (vn) is a subsequence of (un). - If (un) converges to l, any subsequence also converges to l. If sequences extracted from (un) all converge to the same limit l, we can conclude that (un) converges to l if all un is a term of one of the extracted sequences studied. For example, if (u2n) and (u2n + 1) converge to l, then (un) converges to l. • Bolzano-Weierstrass theorem From any bounded sequence of reals, we can extract a convergent subsequence. V Suites de Cauchy • Definition A sequence (un) is Cauchy if, for any positive ε, there exists a natural integer n0 for which, whatever the integers p and q greater than or equal to n0, we have | up − uq | <ε. Be careful, p and q are not related. • Property A sequence of real numbers, or of complexes, converges if, and only if, it is Cauchy SPECIAL SUITES I Arithmetic and geometric sequences • Arithmetic sequences A sequence (un) is arithmetic of reason r if: ∀ n∈N un + 1 = un + r General term: un = u0 + nr. Sum of the first n terms: • Geometric sequences A sequence (un) is geometric of reason q ≠ 0 if: ∀ n∈N un + 1 = qun. General term: un = u0qn Sum of the first n terms: II Recurring suites • Linear recurrent sequences of order 2: - Such a sequence is determined by a relation of the type: (1) ∀ n∈N aUn + 2 + bUn + 1 + cUn = 0 with a ≠ 0 and c ≠ 0 and knowledge of the first two terms u0 and u1. The set of real sequences which satisfy the relation (1) is a vector space of dimension 2. We seek a basis by solving the characteristic equation: ar2 + br + c = 0 (E) - Complex cases a, b, c If ∆ ≠ 0, (E) has two distinct roots r1 and r2. Any sequence satisfying (1) is then like : where K1 and K2 are constants which we then express as a function of u0 and u1. If ∆ = 0, (E) has a double root r0 = (- b) / 2a. Any sequence satisfying (1) is then type: - Case a, b, c real If ∆> 0 or ∆ = 0, the form of the solutions is not modified. If ∆ <0, (E) has two conjugate complex roots r1 = α + iβ and r2 = α − iβ that we write in trigonometric form r1 = ρeiθ and r2 = ρe-iθ Any sequence satisfying (1) is then of the type: • Recurrent sequences un + 1 = f (un) - To study such a sequence, we first determine an interval I containing all the following values. - Possible limit If (un) converges to l and if f is continuous to l, then f (l) = l. - Increasing case f If f is increasing over I, then the sequence (un) is monotonic. The comparison of u0 and u1 makes it possible to know if it is increasing or decreasing. - Decreasing case f If f is decreasing over I, then the sequences (u2n) and (u2n + 1) are monotonic and of contrary Made by LEON
Math · Physics · Computer science
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Our students from Douala evaluate their Physics teacher.

To ensure the quality of our Physics teachers, we ask our students from Douala to review them.
Only reviews of students are published and they are guaranteed by Apprentus. Rated 4.8 out of 5 based on 164 reviews.

CCVX + James Boswell Entrance Exams Preparation (Physics) (Groningen)
Bibek
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My daughter had private tutoring for the Physics CCVX exam with Bibek, and we are extremely pleased with the experience. Bibek is a very knowledgeable, patient, and understanding tutor who truly focuses on the individual needs of the student. He adapts his teaching methods according to the student’s level and learning style, which helped my daughter gain confidence and improve her understanding of difficult concepts. Bibek was highly motivating and supportive throughout the process, encouraging her to stay focused and positive even under pressure. My daughter had a very tight deadline to pass the exam, and Bibek handled this challenge with excellent organisation and clear planning. He structured the lessons efficiently, prioritised key topics, and ensured that time was used effectively. Thanks to his guidance and dedication, my daughter was able to achieve her goal within a limited timeframe. Bibek demonstrates all the important qualities of a great tutor: strong subject knowledge, adaptability, clear communication, motivation, organisation, and genuine commitment to the student’s success. I would highly recommend him to any student looking for high-quality physics tutoring.
Review by MARYAM
SAT exam practice and preparation ( mathematics ) (Tunis)
Rania
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Outstanding Tutor – Highly Recommend! Rania has been an incredible tutor for my daughter, helping her build confidence and truly understand the material in her AP Pre-Calculus class. She has a gift for explaining complex concepts in a clear, patient, and engaging way. My daughter actually looks forward to her sessions and has shown noticeable improvement—not just in grades, but in her overall attitude toward math. Rania is professional, reliable, and genuinely cares about her students’ success. We’re so grateful for her guidance and would absolutely recommend her to any student looking to excel in math!
Review by ALEJANDRA
Private lessons in Math, Physics, Chemistry and SVT (Luxembourg)
Raef
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so lucky to have found this amazing teacher! He explains everything with so much patience and clarity that even the most difficult topics start to feel simple. I noticed a big improvement in my maths level and I love the most how encouraging and supportive he is—he never makes you feel bad for not understanding, instead he finds new ways to explain until it clicks. Thanks to him, I’ve gained so much confidence in maths and I actually enjoy learning now. If you’re looking for a tutor who truly cares about his students’ success, I highly recommend him!
Review by NAGHAM
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