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• Existence of a Solution in the Open Interval (0, 1) for a Cubic Equation with Real Coefficients
• Lipschitz Continuity and Bounded Derivatives of Differentiable Functions
• Convergence of Sequences Given a Quadratic Sum Condition
• Divergence of Harmonic Series and Sequence Behavior at Infinity
• Boundedness of Continuous and Periodic Functions on $\mathbb{R}$
• Fixed Point Theorem for Continuous Functions on a Closed Interval
• Nilpotent matrix and trace
• Computing $\lim\limits_{n\to+\infty}\sum_{p=n+1}^{kn} \frac1 p$ for $k > 1$
• Is the endomorphism $P(X)\mapsto P(X+1)-P(X)$ diagonalizable?
• Non-Periodicity of a Differentiable Function with a Non-Vanishing Derivative

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• Diagonalization
• Eigenvalue
• Extreme Value Theorem
• Fundemental Theorem of Algebra
• Intermediate Value Theorem
• Linear Algebra
• Lipschitz Continuous Function
• Mean Value Inequality
• Mean Value Theorem
• Nilpotent Matrix
• Rolle's Theorem
• Sequences

About this site

• Founded to provide a simple and free online Problem Book.
• Various mathematical notions and chapters are visited through solving problems and exercises with different difficulties.
• The content is intended for undergraduate students (and more generally for mathematics enthusiasts) to practice solving problems as well as for teachers as a source of exercises and problems to enrich their lessons.
• Some hints, short or complete answers can be provided.
• Any suggestions for a problem or exercise or requests for a hint or answer to any questions are welcome. So don’t hesitate to post a comment or to email me at sami.ben.romdhane@zohomail.com

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All Posts

• 2024 Aug 13 – Existence of a Solution in the Open Interval (0, 1) for a Cubic Equation with Real Coefficients
• 2024 Aug 13 – Lipschitz Continuity and Bounded Derivatives of Differentiable Functions
• 2024 Aug 12 – Convergence of Sequences Given a Quadratic Sum Condition
• 2024 Aug 12 – Divergence of Harmonic Series and Sequence Behavior at Infinity
• 2024 Aug 08 – Boundedness of Continuous and Periodic Functions on $\mathbb{R}$
• 2024 Aug 08 – Fixed Point Theorem for Continuous Functions on a Closed Interval
• 2024 Aug 08 – Nilpotent matrix and trace
• 2024 Aug 07 – Computing $\lim\limits_{n\to+\infty}\sum_{p=n+1}^{kn} \frac1 p$ for $k > 1$
• 2024 Aug 07 – Is the endomorphism $P(X)\mapsto P(X+1)-P(X)$ diagonalizable?
• 2024 Aug 07 – Non-Periodicity of a Differentiable Function with a Non-Vanishing Derivative