The Essential and Expanded Guides to Calculus Limits

Our guides include 11 examples on average when a concept is first introduced. Each example is explained with a step-by-step solution. The examples in each section are presented in order of ascending complexity. Therefore, you can ease your way into each concept and technique as they are presented.

Often, there is not enough class time to cover the variety of examples needed to master new concepts and techniques. Considering how busy you are outside of class with homework and extracurriculars, scheduling time with the teacher, classmates, or a tutor to review material and work through additional examples can be quite difficult.

Professional tutors typically charge $50 per hour or more. Consider that a tutor would spend 7 to 9 hours working through all of the examples in our guides. That is a $350 to $450 value. You can master limits at your own pace and in any location with our guides for $39.95 or less!

Master Calculus Limits with over 150 examples with step-by-step solutions.

Master the Limits of Polynomial Functions, Rational Functions, and Functions Involving Radicals

Master Direct Substitution, Cancellation, and Rationalization and understand when each technique can be applied

Master the Properties of Limits, Continuity, and Infinite Limits

Master One-Sided Limits

Understand when the “Limit Does Exist”

Understand when the “Limit Does Not Exist”

Understand Continuity at a point, one-sided, on an interval, and everywhere

Understand Indeterminate Forms

Understand Removable and Nonremovable Discontinuities

Understand Vertical Asymptotes

Understand Infinite Limits

Master Calculus Limits with over 200 examples with step-by-step solutions.

Master the Limits of Polynomial Functions, Rational Functions, Functions Involving Radicals, and Trigonometric Functions

Master Direct Substitution, Cancellation, Rationalization, and Special Limits and understand when each technique can be applied

Master the Properties of Limits, Continuity, and Infinite Limits

Master One-Sided Limits

Understand when the “Limit Does Exist”

Understand when the “Limit Does Not Exist”

Understand Continuity at a point, one-sided, on an interval, and everywhere

Understand Indeterminate Forms

Understand Removable and Nonremovable Discontinuities

Understand Vertical Asymptotes

Understand Infinite Limits

Master Calculus Limits with over 200 examples with step-by-step solutions.

Master the Limits of Polynomial Functions, Rational Functions, Functions Involving Radicals, and Trigonometric Functions

Master Direct Substitution, Cancellation, Rationalization, and Special Limits and understand when each technique can be applied

Master the Properties of Limits, Continuity, and Infinite Limits

Master One-Sided Limits

Understand when the “Limit Does Exist”

Understand when the “Limit Does Not Exist”

Understand Continuity at a point, one-sided, on an interval, and everywhere

Understand Indeterminate Forms

Understand Removable and Nonremovable Discontinuities

Understand Vertical Asymptotes

Understand Infinite Limits

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An intuitive understanding of the limiting process.

Calculating limits using algebra.

Estimating limits from tables of data.

Asymptotic and unbounded behavior

Describing asymptotic behavior in terms of limits involving infinity (infinite limits).

Continuity as a property of functions

An intuitive understanding of continuity. (The function values can be made as close as desired by taking sufficiently close values of the domain.)

Understanding continuity in terms of limits.

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