Math Problem Statement

The image contains exercises on limits, continuity, differentiability, and inverse functions in calculus, intended for a high school calculus course (2nd year BAC PC, Tunisia). The exercises involve evaluating limits, checking continuity, studying differentiability, and determining the inverse of functions.

Solution

The exercises you've uploaded involve calculus topics, including limits, continuity, differentiability, and inverse functions. Let's break down the problems in each exercise:

Exercise 1

  1. Limits: Evaluate the limits as x→0x \to 0.
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Math Problem Analysis

Mathematical Concepts

Limits
Continuity
Differentiability
Inverse Functions

Formulas

Limit as x approaches a value
Continuity check at a point and over an interval
Derivative of a piecewise function
Inverse function determination and differentiation

Theorems

Limit definition and properties
Continuity theorem
Differentiability theorem
Inverse function theorem

Suitable Grade Level

Grade 12 or final year high school (advanced calculus level)

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