Math Problem Statement

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Les réponses

Solution

I can analyze the image and provide you with detailed solutions to the mathematical problems listed. Let me extract and address each part step by step.

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Math Problem Analysis

Mathematical Concepts

Continuity and differentiability of functions
Limits and asymptotic behavior
Series and convergence
Monotonicity and sequences

Formulas

lim_{x→a} f(x)
f(a) = a^2 arctan(1/a)
Σ(1/k^2) for series convergence

Theorems

L'Hopital's Rule for limits
Monotonicity and boundedness criterion for convergence
Fundamental theorem of calculus for differentiability

Suitable Grade Level

Undergraduate Level (Calculus I/II)