Introduction
Precalculus
Getting Started
Calculus 1
1. Limits
3. Derivatives
5. Applications of Derivatives
6. 1. Increasing and Decreasing Function
  2. Minimum and Maximum Values
7. Integrals
8. 1. Indefinite Integrals
  2. Computing Indefinite Integrals
  3. Substitution Rule for Indefinite Integrals
  4. Area Problem
Calculus 2
1. Integration Techniques
2. 1. Integration by Parts
  2. Integrals Involving Trig Functions
  3. Trig Substitutions
  4. Partial Fractions
  5. Integrals Involving Roots
  6. Integrals Involving Quadratics
3. Parametric Equations and Polar Coordinates
4. 1. Differentiation Formulas
  2. Product and Quotient Rule
  3. Chain Rule
  4. Implicit Differentiation
  5. Higher Order Derivatives
  6. Logarithmic Differentiation
5. Series and Sequences
6. 1. Indefinite Integrals
  2. Computing Indefinite Integrals
  3. Substitution Rule for Indefinite Integrals
  4. Area Problem
7. Vectors
8. 3-Dimensional Space
Calculus 3
1. LimitThree Dimensional Coordinate Systems
2. 1. Equations of Lines
  2. Equations of Planes
  3. Quadratic Surfaces
  4. Functions of Multiple Variables
3. Partial Derivatives
4. 1. Higher Order Partial Derivatives
  2. Differentials
  3. Chain Rule
  4. DirectioChain Rulenal Derivatives
  5. Gradient
5. Multiple Integrals
6. 1. Iterated Integrals in Cylindrical Coordinates
  2. Double Integrals
  3. Double Integrals in Polar Coordinates
  4. Triple Integrals in Spherical Coordinates
  5. Change of Variables
  6. Surface Area
7. Line Integrals
8. 1. Line Integrals With Respect to Arc Length
  2. Double Integrals in Polar Coordinates
  3. Line Integrals With Respect to x and y
  4. Line Integrals of Vector Fields
  5. Fundamental Theorem of Line Integrals
  6. Conservative Vector Fields
  7. Potential Functions
  8. Green's Theorem
9. Surface Integrals
10. 1. Parametric Surfaces
  2. Surface Integrals
  3. Surface Integrals of Vector Fields
  4. Stokes' Theorem
  5. Divergence Theorem
Cheatsheet

Infinite Limits

Infinite Limits

An infinite limit is a type of limit that describes how a function behaves as the input values approach a specific point from one side or the other, but never actually reach that point. This can occur if the function has an unbounded output value as the input approaches the point, or if the function becomes undefined at the point.

In general, an infinite limit is represented by the symbol ±∞, where the sign indicates whether the limit is approached from the left or the right. For example, if a function f(x) has an infinite limit as x approaches a point a from the left, this can be written mathematically as follows:

$$ \lim_{x \to a^-} f(x) = -\infty $$

Similarly, if a function f(x) has an infinite limit as x approaches a point a from the right, this can be written mathematically as follows:

$$ \lim_{x \to a^+} f(x) = \infty $$

In both cases, the symbol ±∞ indicates that the function has an unbounded output value as the input approaches the point a, but never actually reaches it. Infinite limits are often encountered in calculus when working with functions that have vertical asymptotes or other types of singularities at certain points in their domain.

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