CALCULUS 1

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CALCULUS 1

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REVIEW OF THE BASICS

Multiplication and Division of Fractions

Addition and Subtraction of Fractions

Functions of Real Numbers

Domain of a Function

Composition of Functions

Inverse Functions

LIMITS AND CONTINUITY

Notion of Limit

Four Basic Limits

THE DERIVATIVE

Derivatives Part 1

Derivatives part 2

Implicit Differentiation

Logarithmic Differentiation

Derivatives of Logarithmic and Exponential Functions

Derivatives of Trigonometric and Inverse Trigonometric Functions

L’Hopital’s Rule

L’Hopital’s Rule Part 2

Indeterminate Forms

APPLICATIONS

Increasing and Decreasing Functions

Relative Maximum and Minimum

Second Derivative Test

Absolute Maximum and Minimum

Concavity and Inflection Points

Local Linear Approximations

Related Rates Part 1

Related Rates Part 2

Error Propagation

ANTIDERIVATIVES

Antiderivatives

Integration by Substitution

Area as a Limit: Riemann Sums

The definite Integral

Area Between Curves

Area Between Curves Part 2

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