Math Doubts

Limits

The value of a function as the input approaches to some value is called limit.

Limit is a basic mathematical concept for learning calculus and it is useful determine continuity of function and also useful to study the advanced calculus topics derivatives and integrals.

Basics

There are two basic concepts to understand the concept of limits clearly in calculus.

  1. Approach
  2. Limit

Representation

$x$ is a variable. A function is formed in terms of $x$ and it is written as $f{(x)}$ mathematically. The function $f{(x)}$ gives a value for every value of $x$. If $x = a$ then the value of function is $f{(a)}$.

Remember, the limit is not the value of function $f{(x)}$ when $x = a$, and it is a value of the function when the value of $x$ closer to $a$. The closer in calculus is denoted by symbol $\to$. Therefore, $x$ closer to $a$ is denoted by $x \to a$. It is read as $x$ tends to $a$ or $x$ approaches $a$.

In calculus, limit is symbolically represented by $\lim$. The limit of $f{(x)}$ is written as $\lim f{(x)}$ but the limit of function is calculated when $x$ approaches $a$. considering all factors, the limit of function $f{(x)}$ when $x$ tends to $a$ is written in mathematically as follows.

$\large \displaystyle \lim_{x \,\to\, a}{\normalsize f{(x)}}$

Take the limit of function $f{(x)}$ is equal to $L$ when $x$ approaches $a$.

$L \,=\, \large \displaystyle \lim_{x \,\to\, a}{\normalsize f{(x)}}$

Rules

Learn list of properties and standard results in limits to use them as formulas while evaluating the limit of any function in calculus.

Problems

List of limits problems with solutions for leaning and practicing.



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