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# Calculus 1 Fundamentals: Limits & Derivatives

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### Overview

Master the building blocks of Calculus:Â  Limits & Derivatives

Section 1 -Â LIMITS

• Concept of Limits:Â For making you familiarÂ withÂ the notion of the Limit.
• Existence of Limits:Â Introduction to the Left-Hand Limit and the Right-Hand Limit.
• Algebra of Limits:Â Addition, Subtraction, Multiplication, and Division in Limits.
• Lâ€™Hospital Rule: A handy toolÂ to circumventÂ the common indeterminate forms when computingÂ limits.
• The Sandwich Theorem:Â To evaluate limits of functions that can't be computed at a given point.
• Limits of Trigonometric Functions:Â To cover the importantÂ limit identities ofÂ trigonometric functions.
• Limits at Infinity:Â To evaluate limits at points tending to positive and negative infinity.

Section 2Â -Â DERIVATIVES

• Concept of Derivatives:Â Meaning of the term "Derivative" in Mathematics.
• First Principle of Derivatives:Â The conventional way of computing derivatives.
• Algebra of Derivatives:Â Addition, Subtraction, Multiplication, and Division in Derivatives.
• Derivatives of common functions:Â To set you free toÂ calculate the derivative of combination of any functions.
• The Chain Rule:Â ToÂ calculate the derivatives of composite functions no matter howÂ complex they are.

### Syllabus

• Calculus Fundamentals : Overview
• Introduction to Limits
• Concept of Limits
• Existence of Limits
• Examples
• Algebra of Limits
• The L'Hospital Rule
• The Sandwich Theorem
• Limits of trigonometric functions
• Limits at Infinity
• Miscellaneous Examples-Limits
• Introduction to Derivatives
• Concept of Derivatives
• First principle of Derivative
• Algebra of Derivatives
• Derivative of common functions
• The Chain rule
• Miscellaneous examples-Derivatives

Tanmay Varshney

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