Algebra Grade 10. Limit and continuity of a function. Derivative and its applications. Collection 1

Embark on an exciting journey through algebra! Our "Algebra Grade 10. Limit and continuity of a function. Derivative and its applications" course offers a dynamic learning experience that brings these advanced mathematical concepts to life. Through interactive lessons, quizzes, and engaging activities, students will gain a deep understanding of limits, continuity, derivatives, and their practical applications.

Why choose our course:

• Interactive tests: Test your knowledge and reinforce learning with engaging and challenging quizzes.
• Expertly crafted content: Developed by experienced educators to ensure high-quality and effective learning.
• Focus on mathematical analysis: Encourage students to analyze functions, apply mathematical properties, and develop logical reasoning.

Course Modules

Module 1: Limit and continuity of a function. Derivative and its applications

• §32. Limit of a Sequence. Basic Theorems on the Limit of a Sequence. The Concept of the Limit of a Function at Infinity (Part 1)
• §33. Limit and Continuity of a Function at a Point (Parts 1, 2)
• §34. Derivative of a Function. Derivatives of the Simplest Functions (Parts 1, 2)
• §35. Physical and Geometric Meaning of the Derivative (Parts 1, 2)
• §36. Rules of Differentiation. Table of Derivatives (Parts 1, 2)
• §37. Derivative of a Composite Function (Parts 1, 2)
• §38. Criteria for a Function to be Constant, Increasing, or Decreasing (Parts 1, 2)
• §39. Extrema of a Function (Parts 1, 2)
• §40. Application of the Derivative for Function Analysis and Graphing (Part 1)
• §41. Greatest and Least Value of a Function on an Interval (Parts 1, 2)
• §42. Application of the Derivative to Solving Equations and Inequalities and Proving Inequalities (Part 1)
• §43. Asymptotes of a Function Graph
• §44. Second Derivative. Function Convexity and Inflection Points. Application of the Second Derivative for Function Analysis and Graphing

Expected Learning Outcomes

• Formulates the definitions of the limit and continuity of a function at a point.
• Formulates the basic properties of the limit of a function and uses them to find the limits of given functions.
• Explains the geometric and physical meaning of the derivative.
• Formulates the definition of the derivative of a function at a point, differentiation rules, sufficient conditions for a function to be increasing or decreasing, and necessary and sufficient conditions for a function's extremum.
• Finds the angular coefficient of the tangent to a function's graph at a given point.
• Finds the derivatives of functions.
• Applies the derivative to find the intervals of monotonicity and extrema of a function.
• Finds the greatest and least value of a function.
• Analyzes functions using the derivative and graphs them.
• Solves applied problems involving finding the greatest and least values of real quantities.
• Applies the results of function analysis using the derivative to solve equations, inequalities, and prove inequalities.
• Describes the concepts of function convexity and inflection points.
• Applies the second derivative to find the intervals of convexity and inflection points of a function.
• Analyzes functions using the first and second derivatives and uses the results to graph functions.
• Applies the derivative to solve problems, including those with practical applications.

By the end of this course, students will have a thorough understanding of limits, derivatives, and their applications, equipping them with essential tools for advanced mathematics.