# Calculus I Essentials

# Calculus I Essentials

- COURSE CONTENTS
- TEACHER
- COMMUNITY
- FAQ
- BACK TO TOP

## What you'll learn in this course

Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.

More- Lesson Intro
- Functions vs. Equations
- What are Functions?
- Exercise - Inputs and Outputs
- Domain and Range
- Exercise - Domain and Range
- What Functions are Not
- Exercise - Vertical Line Test
- Combinations and Compositions
- Exercise - Combinations
- Final Assignment

- What Is It?
- Exercise - Definition of the vertical line test
- Graph One
- Graph Two
- Graph Three
- Graph Four
- Exercise - Vertical line test rules
- Wrap Up
- Final Assignment

- Lesson Intro
- Limits
- Exercise - Limits
- Solving for Limits
- Exercise - Solving Limits
- Infinite Limits
- Exercise - Infinite Limits
- Examples
- Exercise - General Limits
- Final Assignment

- Prove It
- Game Plan
- Exercise - The definition of the limit
- Left Hand Limit
- Right Hand Limit
- Proven
- Exercise - The general limit
- Final Assignment

- Game Plan
- Show the Truth
- Definition of the Limit
- Exercise - The precise definition of the limit
- Execution
- Conclusion
- Exercise - Sample problem
- Final Assignment

- Lesson Intro
- Rate of Change
- Exercise - Rate of Change
- Tangent and Secant
- Exercise - Tangent vs. Secant Line
- Calculating the Tangent Line
- Exercise - Calculating the Tangent Line
- Definition of the Derivative
- Exercise - Definition of a Derivative
- Example
- Final Assignment

- Game Plan
- f (a+h)
- f (a)
- Simplify
- Cancel Then Finish
- Exercise - Using the definition of the derivative
- Final Assignment

- Game Plan
- Plug It In
- Simplify
- Collect Terms
- Simplify Some More
- Slope Found
- Finding the Point
- Final Answer
- Exercise - Summary
- Final Assignment

- Game Plan
- (x)(sin y)
- Exercise - Taking The Derivative of Y
- (y)(sin x)
- Simplify
- Separate
- Final Answer
- Exercise - Solving Your Final Answer
- Final Assignment

- Lesson Intro
- Optimization
- Exercise - Local Maximum and Minimum
- Solving Optimization Problems
- Exercise - Solving Optimization Problems
- Applied Optimization
- Exercise - Applied Optimization
- Example: Optimizing the Surface Area ...
- Exercise - Example: Optimization
- Final Assignment

- Lesson Intro
- Implicit Differentiation
- Exercise - Implicit Differentiation
- Example: Implicit Differentiation
- Exercise - Example: Implicit Differentiation
- Related Rates
- Exercise - Related Rates
- Related Rates Example: Spherical Balloon
- Exercise - Example: Spherical Balloon
- Related Rates Example: Leaning Ladder
- Exercise - Example: Leaning Ladder
- Wrapping Up
- Final Assignment

## About your teacher

Whether you’re starting your first semester of calculus, or cramming for your final exam, integralCALC will help you quickly build skills with simple, step-by-step lessons.

Krista King (founder of integralCALC) worked as a calculus tutor while she was a student at the University of Notre Dame. After graduation, she started integralCALC to serve as a resource for calculus students. Since the beginning of 2010, Krista’s calculus lessons have helped students around the world and she continues to publish lessons regularly.

More## Don't take our word for it, ask your future coursemates!

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**1712 students** already learning together. And
more are joining every day! Students at Curious love to learn together and
help each other out. Meet a few of your virtual coursemates below.

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