Circular Measure HCI Cheers Ivan (11)| Jeremy (02) 4O1 Copyright © 2010 HCICheers Pte Ltd. All Rights Reserved. For Educational Purposes only In conjunction with… Ω β α π κ μ λ ξ θ Binomial Theorem + - x ÷ )¯¯¯ Differentiation Integration Trigonometry

Introduction –Pascal’s Triangle –Thus, Binomial Theorem n=0 n=1 n=2 n=3 n=

Binomial Theorem 1. Where When 2. Binomial Theorem

Binomial Theorem (Advanced) Binomial Theorem

Binomial Theorem (Advanced) –Newton's generalized binomial theorem –Around 1665, Isaac Newton generalized the formula to allow real exponents other than nonnegative integers. In this generalization, the finite sum is replaced by an infinite series. –In order to do this one needs to factor out (n−k)! from numerator & denominator in that formula, and replacing n by r which now stands for an arbitrary number, one can define: –Where is the Pochhammer symbol here standing for a falling factorial. Binomial Theorem

Binomial Theorem (Advanced) Binomial Theorem

Video Presentation (Part1) Binomial Theorem

Video Presentation (Part2) Binomial Theorem

Video Presentation (Part3) Binomial Theorem

Circular Measure Formula Circular Measure

Circular Measure Formula Circular Measure

Video Presentation (Part1) Circular Measure

Video Presentation (Part2) Circular Measure

Video Presentation (Part3) Circular Measure

Trigonometrical Functions Differentiation

Diffusing Chain Rule Differentiation of Exponential Functions Differentiation

Laws of Logarithim

Video Presentation (Part1) Differentiation

Video Presentation (Part2) Differentiation

Video Presentation (Part3) Differentiation

Indefinite Integrals Integration

Definite Integrals Integration

Integration of Trigonometric Functions Integration

Integration of Exponential Functions Integration of Logarithmic Functions Integration

Video Presentation (Part1) Integration

Video Presentation (Part2) Integration

Video Presentation (Part3) Integration

Cheers Differentiation - Power Rule

Cheers Differentiation - Chain Rule

Cheers Differentiation - Product Rule

Cheers Differentiation - Quotient Rule

Cheers Differentiation - Trigonometrical Functions

Cheers Differentiation - Trigonometrical Functions

Cheers Differentiation - Diffusing Chain Rule

Cheers Differentiation - Differentiation of Exponential Functions Derivatives of Natural Logarithmic Functions

Cheers Differentiation - Indefinite Integrals

Cheers Differentiation - Integration of Trigonometric Functions

Cheers Differentiation - Integration of Trigonometric Functions

Cheers Differentiation - Integration of Exponential Functions

Cheers Differentiation - Integration of Logarithmic Functions

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Bibliography – – – – Guide Notes Spark Notes Past Formulas Copyright © 2010 HCICheers Pte Ltd. All Rights Reserved. For Educational Purposes only

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