Hello friends I think you have understood the last articles today we are going to study about limits and infinity which you need to study in calculus in grade XII.As you are now familiar with functions, range and domain they are very important to understand the concept of math because these are the basic requirements for studying limits. Now let’s see how to solve limits?
Limit of any function can be defined as the behavior of the function near a particular input. Let’s suppose a function f has the output f(x) to every input x and the function has limit L and an input p. If f(x) is close to L when f(x) is close to p. In simple words we can say as f(x) moves closer to L x moves closer to p. and if we talk about infinity we know that it is impossible to reach there but we still try to reach it. For more on limits visit this.
Limits at infinity is used to describe the behavior of the function with respect to its limit and also describes its behavior as the independent variable increase or decrease without any bound. In actual the value we get from the limit is not the exact value but the value we get is very close to real value or we can say tends to that value.
Limit has a wide application in the world of mathematics. (Also see Upper Limits) It can be applied to simplify the function and also used to find the value of the function. General notation of limit is given below
By the above statement we can say that as x approaches to infinity 1/x approaches to 0. Whenever you see limits you just think of approaching to some value. In mathematical language we can say we are not talking about x tending to infinity. We just know that as x gets bigger, value of the function approaches to 0
Let’s see one example of limit approaching to infinity
y=3x
As x=1 y=3
x=2 y=6
x=3 y=9
x=4 y=12
and so on
x=100 y=3000
Now as x approaches to infinity y approaches to infinity as well. Now we will see one more example
2x2 -5x
2x2 will always tend towards infinity and -5x always tends towards minus infinity so if x will increase where will the function tends?
It will always depend on the value of if x2 will grow more rapidly with respect to x as x increases then the function will surely tend towards the positive infinity.
Now let’s talk about the degree of the function. The degree of the function can be defined as the highest power of variable for example
5x2+6x+7
In this x has highest power 2 so degree of the function will be 2.
By looking at degree of the function we can tell that limit will be positive or negative.
If degree of the function is greater than 0 then limit will always be positive.
If degree of the function is less than 0 then the limit will be 0
This is all about limits at infinity. I hope you have understood all the things in limit at infinity
In upcoming posts we will discuss about Linear Equations and Inequalities and standard deviation of normally distributed random variable. Visit our website for information on 12th biology syllabus Maharashtra board
Limit of any function can be defined as the behavior of the function near a particular input. Let’s suppose a function f has the output f(x) to every input x and the function has limit L and an input p. If f(x) is close to L when f(x) is close to p. In simple words we can say as f(x) moves closer to L x moves closer to p. and if we talk about infinity we know that it is impossible to reach there but we still try to reach it. For more on limits visit this.
Limits at infinity is used to describe the behavior of the function with respect to its limit and also describes its behavior as the independent variable increase or decrease without any bound. In actual the value we get from the limit is not the exact value but the value we get is very close to real value or we can say tends to that value.
Limit has a wide application in the world of mathematics. (Also see Upper Limits) It can be applied to simplify the function and also used to find the value of the function. General notation of limit is given below
By the above statement we can say that as x approaches to infinity 1/x approaches to 0. Whenever you see limits you just think of approaching to some value. In mathematical language we can say we are not talking about x tending to infinity. We just know that as x gets bigger, value of the function approaches to 0
Let’s see one example of limit approaching to infinity
y=3x
As x=1 y=3
x=2 y=6
x=3 y=9
x=4 y=12
and so on
x=100 y=3000
Now as x approaches to infinity y approaches to infinity as well. Now we will see one more example
2x2 -5x
2x2 will always tend towards infinity and -5x always tends towards minus infinity so if x will increase where will the function tends?
It will always depend on the value of if x2 will grow more rapidly with respect to x as x increases then the function will surely tend towards the positive infinity.
Now let’s talk about the degree of the function. The degree of the function can be defined as the highest power of variable for example
5x2+6x+7
In this x has highest power 2 so degree of the function will be 2.
By looking at degree of the function we can tell that limit will be positive or negative.
If degree of the function is greater than 0 then limit will always be positive.
If degree of the function is less than 0 then the limit will be 0
This is all about limits at infinity. I hope you have understood all the things in limit at infinity
In upcoming posts we will discuss about Linear Equations and Inequalities and standard deviation of normally distributed random variable. Visit our website for information on 12th biology syllabus Maharashtra board
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