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# Calculus X: College and AP Calc Test Prep and Tools

Knowvio LLC

Calculus X is the most effective study tool for calculus at the AP or intro college level. It integrates free response questions, concise videos, quizzes, formula sheets, scratch pad and references to make the study process efficient, easy and mobile.

If you’re a busy student, finding enough time to study for each calculus exam is a challenge. We have used the latest developments in educational psychology to build an app that maximizes productivity and helps you learn and do calculus as quickly as possible.

WHAT’S INCLUDED:

-Over 800 multiple choice questions with detailed solutions.

These conceptual based questions help you to learn calculus in a deep and intuitive way. They can all be answered without a calculator, pen or paper; making the study process as mobile as possible.

-Over 75 beautiful 720p videos which solve free response style questions in step-by-step detail.

These concise videos were designed specifically for the mobile device and solve the problems clearly and systematically in order to develop your problem solving intuition. They use narration and detailed visual guidance to increase understanding of the solution method. More video content coming soon.

-Extensive formula sheets accompany each chapter for quick access to all formulas from intro calculus, and all the necessary formulas from pre-calculus. Plus referenc e

-Fun and easy-to-use scratch pad allows you to do calculations on the fly, without the need for pencil and paper.

-Reference materials include: trigonometric identities, differentiation rules, limit laws, key theorem statements, derivatives of all common functions, and more.

WHO THE APP IS FOR:

- Students taking Calculus 1 or Calculus 2 in college

- Students taking AP calculus in high school

- Students studying for exams in different fields who need to review calculus

- Anybody interested in learning calculus

TOPICS COVERED:

---Limits---

Limits Intuition

Limit Operations

Factoring and Limits

Rationalizing and Limits

The Squeeze Theorem

Vertical Asymptotes

Horizontal Asymptotes

Relative Magnitude

One-Sided Limits

---Continuity---

Continuity Intuition

Limit Definition of Continuity

Examples of Continuous Functions

The Composition Theorem

The Intermediate Value Theorem

---Derivatives---

Derivatives Intuition

Limit Definition of the Derivative

Derivative Operations

The Power Rule

The Quotient Rule

Differentiating Trigonometric Functions

The Chain Rule

Differentiating Exponential and Logarithmic Functions

Logarithmic Differentiation

Implicit Differentiation

Tangent Lines

Related Rates

Linear Approximation

Higher Order Derivatives

Maxima and Minima

Optimization

The Mean Value Theorem

L’Hopital’s Rule

---The Integral ---

Antiderivatives

Riemann Sums

Summation Notation

Definition of the Integral

Fundamental Theorem of Calculus

Properties of the Integral

Integral Versus Area

The Integral Function

--Integration Techniques---

Polynomial Integration

Exponential Integration

Trig function integration

Even and odd functions

U-substitution

Bounds and U-substitution

Multiple trig functions

Integration by parts

Trigonometric substitution

Partial fraction decomposition

Discontinuities and absolute values

Improper integrals

---Applications of Integration---

Arc Length

Differential Equations

---Series---

Convergence limit definition

Telescoping series

Geometric series

Harmonic series

p-series

Divergence test

Comparison test

Limit comparison test

Ration test

Root test

Integral test

Alternating series test

Absolute and conditional convergence

---Taylor Series---

Series with variables

Taylor series intuition

Partial Taylor series

Full Taylor series

Shifted Polynomials

Taylor series operations

Radius of convergence

ABOUT US:

Knowvio apps are developed for students by students at the University of Chicago

-More videos

-More formula sheets

-UI tweaks

-Bug fixes

If you’re a busy student, finding enough time to study for each calculus exam is a challenge. We have used the latest developments in educational psychology to build an app that maximizes productivity and helps you learn and do calculus as quickly as possible.

WHAT’S INCLUDED:

-Over 800 multiple choice questions with detailed solutions.

These conceptual based questions help you to learn calculus in a deep and intuitive way. They can all be answered without a calculator, pen or paper; making the study process as mobile as possible.

-Over 75 beautiful 720p videos which solve free response style questions in step-by-step detail.

These concise videos were designed specifically for the mobile device and solve the problems clearly and systematically in order to develop your problem solving intuition. They use narration and detailed visual guidance to increase understanding of the solution method. More video content coming soon.

-Extensive formula sheets accompany each chapter for quick access to all formulas from intro calculus, and all the necessary formulas from pre-calculus. Plus referenc e

-Fun and easy-to-use scratch pad allows you to do calculations on the fly, without the need for pencil and paper.

-Reference materials include: trigonometric identities, differentiation rules, limit laws, key theorem statements, derivatives of all common functions, and more.

WHO THE APP IS FOR:

- Students taking Calculus 1 or Calculus 2 in college

- Students taking AP calculus in high school

- Students studying for exams in different fields who need to review calculus

- Anybody interested in learning calculus

TOPICS COVERED:

---Limits---

Limits Intuition

Limit Operations

Factoring and Limits

Rationalizing and Limits

The Squeeze Theorem

Vertical Asymptotes

Horizontal Asymptotes

Relative Magnitude

One-Sided Limits

---Continuity---

Continuity Intuition

Limit Definition of Continuity

Examples of Continuous Functions

The Composition Theorem

The Intermediate Value Theorem

---Derivatives---

Derivatives Intuition

Limit Definition of the Derivative

Derivative Operations

The Power Rule

The Quotient Rule

Differentiating Trigonometric Functions

The Chain Rule

Differentiating Exponential and Logarithmic Functions

Logarithmic Differentiation

Implicit Differentiation

Tangent Lines

Related Rates

Linear Approximation

Higher Order Derivatives

Maxima and Minima

Optimization

The Mean Value Theorem

L’Hopital’s Rule

---The Integral ---

Antiderivatives

Riemann Sums

Summation Notation

Definition of the Integral

Fundamental Theorem of Calculus

Properties of the Integral

Integral Versus Area

The Integral Function

--Integration Techniques---

Polynomial Integration

Exponential Integration

Trig function integration

Even and odd functions

U-substitution

Bounds and U-substitution

Multiple trig functions

Integration by parts

Trigonometric substitution

Partial fraction decomposition

Discontinuities and absolute values

Improper integrals

---Applications of Integration---

Arc Length

Differential Equations

---Series---

Convergence limit definition

Telescoping series

Geometric series

Harmonic series

p-series

Divergence test

Comparison test

Limit comparison test

Ration test

Root test

Integral test

Alternating series test

Absolute and conditional convergence

---Taylor Series---

Series with variables

Taylor series intuition

Partial Taylor series

Full Taylor series

Shifted Polynomials

Taylor series operations

Radius of convergence

ABOUT US:

Knowvio apps are developed for students by students at the University of Chicago

➜ What's new in version 1.4.1

-More quiz content-More videos

-More formula sheets

-UI tweaks

-Bug fixes