# Calculus I

Video Math Teacher provides Calculus I tutor services for the two major branches on Calculus I: Differential Calculus and Integral Calculus. Calculus is the study of change in the same way that geometry is the study of shape and algebra is the study of equations. Our Calculus I tutorial videos help students learn at their own pace. From beginning to end, our videos and lessons allow students to first test themselves and find out where exactly help is needed. Once the student has found their problem areas, they can then begin to search through our Calculus I videos to find the help that they need.

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All Calculus I Lessons Include

- Test Yourself
- Basic Mathematics
- Real Numbers
- Cartesian Plane
- Lines

- Functions and Limits
- Functions and Graphs
- More on Graphs of Functions
- Trigonometric Functions
- Setting Up Functions
- Limit of a Function at a Point
- Theorems on Limits
- Limits that Involve Infinity
- Continuity

- The Derivative
- Rate of Change of a Function, Tangent to a Graph, Instantaneous Velocity
- The Derivative
- Rules of Differentiation I - Power and Sum Rules
- Rules of Differentiation II - Product and Quotient Rules
- Derivatives of the Trigonometric Functions, Some Preliminary Limit Results
- Rules of Differentiation III - Chain Rule
- Higher-Order Derivatives.
- Implicit Differentiation
- Rules of Differentiation IV - Extended Power Rules
- Differentials and Linear Approximation
- Newton's Method

- Applications of the Derivative
- Rectilinear Motion and the Derivative
- Related Rates
- Extrema of Functions
- Rolle's Theorem and the Mean Value Theorem
- Graphing and the First Derivative
- Graphing and the Second Derivative
- Further Applications of Extrema
- Applications of the Derivative in Economics

- The Integral
- Antiderivatives
- Indefinite Integrals and the u-Substitution
- Sigma Notation
- Area Under a Graph
- Definite Integral; Definition of a Definite Integral
- Properties of the Definite Integral
- Fundamental Theorem of Calculus
- Definite Integral; Definition of a Definite Integral

- Applications of the Integral
- Area and Area Bounded by Two Graphs
- Volumes by Slicing
- Solids of Revolution.
- Arc Length
- Surfaces of Revolution
- Average Value of a Function and the Mean Value Theorem for Integrals
- Surfaces of Revolution
- Work
- Liquid Pressure and Force
- Centers of Mass
- Applications to Biology and Business