Table of Contents
Limit and Continuity Meaning
1. Limit
A limit is a point at which a function becomes discontinuous. This point is also known as a discontinuity point.
There are two types of discontinuity points:
A point of discontinuity where the function value changes abruptly.
A point of discontinuity where the function value changes without a sharp edge.
2. Continuity
A function is continuous at a point if it can be drawn without lifting your pen from the paper. In other words, the function can be drawn as a smooth curve without any breaks or jumps.
Continuity Meaning
Continuity can be defined as a concept that deals with the uninterrupted flow of something. It can be used to refer to time, space, or any other phenomenon that can be measured or experienced. In mathematics, continuity is a property that is used to define differentiable functions. A function is continuous if given any two points within the function’s domain, there exists a smooth curve that connects those points.
Types of Discontinuity
There are different types of discontinuity in mathematics:
1. Point discontinuity: A function has a point discontinuity at a certain point in its domain if it is not continuous at that point. A function can have a point discontinuity in either its domain or its range.
2. Jump discontinuity: A function has a jump discontinuity at a certain point in its domain if it is discontinuous at that point, but the discontinuity is not a result of the function not being continuous at that point. Rather, the discontinuity is a result of the function taking on two different values at that point. A function can have a jump discontinuity in either its domain or its range.
3. Hiatus discontinuity: A function has a hiatus discontinuity at a certain point in its domain if it is discontinuous at that point, but the discontinuity is not a result of the function not being continuous at that point. Rather, the discontinuity is a result of the function taking on two different values at that point and not having a value in between. A function can have a hiatus discontinuity in either its domain or its range.
4. Step discontinuity: A function has a step discontinuity at a certain point in its domain if it is discontinuous at that point, but the discontinuity is not a result of the function not being continuous at that point. Rather, the discontinuity is a result of the function taking on two
Limit
A limit is the maximum permitted value of a quantity.
The speed limit on a highway is the maximum speed that is allowed.
The limit on a bank account is the maximum amount that can be deposited.
Important Points
The key points to remember are:
– Hemp is a sustainable and environmentally friendly crop
– Hemp has a wide range of uses
– Hemp can be used to produce a range of products, including food, fuel, clothing and building materials
One – Sided Limit
There is a one sided limit for the sum of two consecutive terms in a geometric sequence. If the limit exists, then it is less than or equal to the sum of the two terms.
Properties of Limit
The limit of a function is a real number that the function approaches as the input approaches a certain value. The limit is also the value that the function equals at that certain value.
