## What is the relationship between limits and continuity?

How are limits related to continuity? The definition of continuity is given with the help of limits as, a function f with variable x is continuous at the point “a” on the real line, if the limit of f(x), when x approaches the point “a”, is equal to the value of f(x) at “a”, that means f(a).

## What is the basic concept of limit and continuity?

A function of two variables is continuous at a point if the limit exists at that point, the function exists at that point, and the limit and function are equal at that point.

**How can we apply limits of a function in real life?**

Similarly, if you drop an ice cube in a glass of warm water and measure the temperature with time, the temperature eventually approaches the room temperature where the glass is stored. Measuring the temperature is a limit again as time approaches infinity.

### What is a real life example of a continuous function?

Suppose you want to use a digital recording device to record yourself singing in the shower. The song comes out as a continuous function.

### What is the difference between limit of function and continuity of function?

A limit is a certain value. Continuity describes the behavior of a function. In calculus, a limit is the first thing you learn, and it is the value that a function of x approaches as its x-value approaches a certain value.

**Why is limit and continuity important?**

The concept of the limit is one of the most crucial things to understand in order to prepare for calculus. A limit is a number that a function approaches as the independent variable of the function approaches a given value. Using limits, we’ll learn a better and far more precise way of defining continuity as well.

#### Why are limits and continuity important?

The concept of the limit is one of the most crucial things to understand in order to prepare for calculus. A limit is a number that a function approaches as the independent variable of the function approaches a given value.

#### Can a function have two limits?

No, if a function has a limit x→y, the limit can only have one value. Because if limx→yf(x)=A and limx→yf(x)=B then A=B.