Limit of Polynomial Function
Limit of the polynomial function are added below, consider a polynomial function,
f(x) = a0 + a1x + a2x2 + … + anxn
Here, a0, a1, … , an are all constants. At any point x = a, the limit of this polynomial function is
lim x ⇢ a f(x) = lim x ⇢ a [a0 + a1x + a2x2 + . . . + anxn]
= lim x ⇢ a a0 + a1lim x ⇢ a x + a2lim x ⇢ a x2 + . . . + anlim x ⇢ a xn
lim x ⇢ a a0 + a1a + a2a2 + . . . + anan
lim x ⇢ a = f(a)
Limits in Calculus
Limits in maths are defined as the values approaching the output for the given input values of a function. Limits are used in calculus and mathematical analysis for finding the derivatives of the function. They are also used to define the continuity of the function.
The limit of any function is also used to find the integral of the function. The integral are of two types, Indefinite Integral, and Definite Integral, in definite integral we use the concept of upper limit and lower limit to find the answer to the definite integral. A function can reach a particular value from more than one path and the value of the function at that particular point is called the limit of the function at that point. Suppose we are given a function f(x) and when x approaches a the function approaches A this i represented using the limit as:
lim x ⇢ a f(x) = A
In this article, we will learn the introduction to limits, properties of limits, limits, and continuity, and others in detail.
Table of Content
- What Are Limits in Calculus?
- Limits Definition
- Formula of Limit
- Types of Limits
- Infinite Limits
- Limits at Infinity
- Properties of Limits
- Algebra of Limit
- Limits and Functions
- Limit of Polynomial Function
- Limit of Rational Function
- Limits of Complex Functions
- Limits of Exponential Functions
- Limit of a Function of Two Variables
- Calculating Limits
- Examples of Limits
- Limits and Derivatives Class 11
- Resources Related to Limits:
- Practice Questions on Limits in Calculus
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