Calculus Formulas

Limit Formulas

Concept of a Limit


Limit from the Left

Limit from the Right


Limit of Positive Infinity

Limit of Negative Infinity


Limit as x Approaches Infinity

Limit as x Approaches Negative Infinity


Limit of a Constant

Limit of a Sum

Limit of a Product

Limit of a Quotient

Limit of a Power

Limit of a Function

g can be a root, a log, sin, cos, tan, etc.

Limit of a Radical

Limit of a Logarithm


L'Hôpital's Rule

L'Hopital's Rule or L'Hopital's Rule

L'Hopital's Rule


Continuity Formulas

Continuous Function at a Point

Terms

Continuity Formulas

Continuous Function at a Point


Directional Continuity

Left-Continuous Function

Right-Continuous Function

Right-Continuous Function

Left-Continuous Function


Discontinuity

Removable Discontinuity

Removable Discontinuity or Removable Discontinuity

Jump Discontinuity

Jump Discontinuity

Essential Discontinuity

Essential Discontinuity


Derivative Formulas

u and v are functions of x.

a, e and k are constants (real numbers)

Derivative of a Constant

Derivative of Constant Multiple

Derivative of x

Power Rule

Derivative of a Radical

Derivative of an Irrational Function

Derivative of a Sum or Difference

Derivative of a Product

Derivative of a Logarithmic Function

Derivative of a Natural Logarithmic Function

Derivative of a Secant Function

Derivative of a Cosecant Function

Functional Power Rule


Chain Rule

Derivative of an Implicit Function


Integrals Formulas

Integral of x

Integral of a Constant

Integral of an Exponent

Integral

Exponential Integral

Exponential Integral

Integral

Cosine Integral

Tangent Integral

Cotangent Integral

Arcsine Integral

Arctangent Integral


Integration by Parts

Integration by Parts


Integration by Substitution

Integration by Substitution


Change of Variables

Change of Variable

Change of Variable

Change of Variable

Change of Variable

If Rational is even:

Change of Variable

If Rationalis not even:

Change of Variable


Definite Integral

Barrow's Rule

Property of the Definite Integral

Property of the Definite Integral

Property of the Definite Integral

Property of the Definite Integral

Property of the Definite Integral

Property of the Definite Integral

Definite Integral

Volume