Math Problem Statement

Exam__Analyse_mathématique__S1__N__20-21[1].pdf

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pdf_text[:1000] # Show the first 1000 characters of the extracted textThe document you uploaded appears to be a mathematical exam, written in French, focused on analysis (likely calculus or mathematical analysis). It contains a series of multiple-choice questions (QCM) related to functions, limits, and other analysis topics. Here are a few excerpts from the text:

  1. Question 1: Concerns the domain of definition for a function f(x)=ln(xx2)f(x) = \ln\left(\frac{x}{x^2}\right).
  2. Question 2: Involves finding the limit limx1((x1)ln(x))\lim_{x \to 1} \left( (x-1) \ln(x) \right).
  3. Question 3: Defines a piecewise function f(x)={2+exif x0ex+1if x>0f(x) = \left\{ \begin{array}{ll} 2 + e^x & \text{if } x \leq 0 \\ e^x + 1 & \text{if } x > 0 \end{array} \right. and asks about its continuity.

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Math Problem Analysis

Mathematical Concepts

Analysis
Calculus
Functions
Limits
Continuity
Piecewise Functions

Formulas

f(x) = \ln\left(\frac{x}{x^2}\right)
\lim_{x \to 1} \left( (x-1) \ln(x) \right)
f(x) = \left\{ \begin{array}{ll} 2 + e^x & \text{if } x \leq 0 \\ e^x + 1 & \text{if } x > 0 \end{array} \right.

Theorems

Domain of Definition of a Function
Limit of a Function
Continuity of Piecewise Functions

Suitable Grade Level

Grades 11-12