Single Variable Calculus

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Functions and Models

Jump into a comprehensive review of various functions from linear to exponential to trigonometric. Refresh how to evaluate different types of specific functions and operations including logarithms and inverse functions. Revisit graphing and calculating zeroes of different polynomial functions.

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FunctionsFree

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Exponential Functions

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Inverse Functions and Logarithms

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Inverse functions

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Logarithms

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Trigonometric functions

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Limits and Derivatives

Push yourself to the limit as you demonstrate knowledge of limits and derivatives. Learn to identify asymptotes, an important skill in function analysis. Analyze functions and determine the limits through calculation.

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Epsilon/Delta Definition of Limits

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Epsilon definition of limit

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Computing Limits Analytically

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Continuity

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Differentiation

Climb the slopes of calculus and dig deep for differentiation. Calculate a function's derivative both at specific points and as another function entirely. Apply rules such as the Quotient, Product, and Chain Rules to calculate derivatives of more complicated functions. Extend your knowledge of derivatives to trigonometric, hyperbolic, transcendental, and inverse functions. Also apply the concept of local linearity to create linear approximations.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Derivatives

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Fundamentals to Differentiation

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Product and Quotient Rules

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Product Rule

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Quotient Rule

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The Chain Rule

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Implicit Differentiation

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Logarithmic Differentiation

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Trigonometric Derivatives

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Derivatives of trigonometric functions

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Inverse trigonometric functions

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Hyperbolic functions

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Linear Approximations and Differentials

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Applications of Differentiation

Use differentiation to determine max and min values, continuity through an interval, concavity of the curvature of a function, landmarks on a graph, and related rates. Continue to apply these techniques into a wide array of applications including finance, physics, chemistry, and when to throw a snowball before it melts too much.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Finding Minimum and Maximum Values

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Mean Value Theorem

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First and Second Derivative Test

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Curve Sketching

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Optimization Methods

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L’Hopital’s Rule

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Related Rates

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Business and Economics Applications

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Newton’s Method

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Integrals

One of the most breakthrough moments in calculus was when it was discovered that integration and derivatives were reverse operations. While derivatives calculate small rates of change, integrals sum all these small changes back up. Begin by applying definite integrals to find area under a curve and indefinite integrals to find antiderivative functions. Learn about Riemann sums to approximate integrals and u-substitution as a method of solving more complex integrals.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

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Re-answering questions correctly will improve your weighted average status.

Antiderivatives and Indefinite Integrals

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Antiderivatives

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Indefinite integrals

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Net Area and Properties of Integrals

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Net area

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Properties of integrals

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Riemann Sums and Definite Integrals

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Definite integrals

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The Fundamental Theorem of Calculus

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Integration by Substitution

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Applications of Integration

As a powerful tool in mathematics, integration can be used in any situation involving change to sum the small changes to find a total, even if those changes are not constant. Apply integration to problems involving total change over time, finding the area of unusual shapes, and even calculating the volume of complex figures. Also explore how integration can be used in other disciplines such as physics to determine values such as center of mass or work performed.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

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Re-answering questions correctly will improve your weighted average status.

Finding Areas Between Curves

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Volume

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The Disk method

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Finding Average Values of a Function

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Integration Techniques

Continue on the path to learn new methods of integration including integration by parts, trigonometric integration, partial fractions, and a revisit of L'Hopital's Rule. Apply these methods to solve more complex integrals, such as finding the area under an unbounded curve in an infinite integral.

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Accuracy is based on your most recent attempt.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

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Re-answering questions correctly will improve your weighted average status.

Fundamentals of Integration

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Integration by Parts

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Trigonometric Integrals

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Trigonometric Substitutions

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Integrating Using Partial Fractions

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Infinite Integrals and L’Hopital’s Rule

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Infinite integrals

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Differential Equations

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Separable Equations

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First Order Linear Equations

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Infinite Sequences and Series

Revisit the concept of the limit and further explore sequences and series. Learn about convergence and divergence. Use different methods, including applying the integral, to test for convergence. Finally, discover power series such as the Taylor and Maclaurin series and their amazing ability to approximate complex functions around a point.

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Accuracy is based on your most recent attempt.

Status

Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Sequences

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Series

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The Integral Test

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The Comparison Tests

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Alternating Series

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Absolute Convergence and the Ratio and Root Tests

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Absolute convergence

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The ratio test

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Power Series

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Taylor Series

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