Items

• imaginary axis

  The vertical line in the complex plane, every point on which corresponds to a complex number having zero real component.
• implicit differentiation

  Is nothing more than a special case of the well-known chain rule for derivatives. The majority of differentiation problems in first-year calculus involve functions y written EXPLICITLY as functions of x.
• implicit function

  Is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments). Thus, an implicit function for in the context of the unit circle is defined implicitly by .
• improper integral

  An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number, or in some instances as both endpoints approach limits.
• increasing function

  A function is "increasing" when the y-value increases as the x-value increases, like this: It is easy to see that y=f(x) tends to go up as it goes along
• increasing sequence

  A sequence (an) is monotonic increasing if an+1≥ an for all n ∈ N. Remarks. The sequence is strictly monotonic increasing if we have > in the definition.
• indefinite integral

  An integral expressed without limits, and so containing an arbitrary constant.
• independent variable

  A variable (often denoted by x ) whose variation does not depend on that of another.
• indeterminate form

  Is an expression involving two functions whose limit cannot be determined solely from the limits of the individual functions.
• index

  It is a power or exponent to which a base number is raised, indicating how many times the base is multiplied by itself.
• induction

  Induction is a logical reasoning process where general conclusions are drawn from specific observations.
• inequality

  The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
• infimum

  The infimum is its greatest lower bound.
• infinite discontinuity

  An infinite discontinuity exists when one of the one-sided limits of the function is infinite. In other words, lim x → c + f ( x ) = ∞ , or one of the other three varieties of infinite limits. If the two one-sided limits have the same value, then the two-sided limit will also exist.
• infinite interval

  An interval is a connected portion of the real line. If the endpoints and are finite and are included, the interval is called closed and is denoted. Intervals involving infinity are also called rays or half-lines. If the finite point is included, it is a closed half-line or closed ray.
• infinite limit

  Infinite limits are those that have a value of ±∞, where the function grows without bound as it approaches some value a.
• infinite sequence

  An infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, - }.
• infinity

  Infinity (symbol: ∞) is a concept describing something without any bound or larger than any natural number. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.
• inflection point

  A point of a curve at which a change in the direction of curvature occurs
• initial condition

  Any of a set of starting-point values belonging to or imposed upon the variables in an equation that has one or more arbitrary constants.
• initial point

  The first point at which a moving target is located on a plotting board
• initial side of the angle

  An angle is in standard position in the coordinate plane if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.
• initial-value problem

  In the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.
• injection

  An injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain
• injective function

  In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain