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# Left and right hand limit

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Limit is a very old concept in the mathematics, and when we talk about Calculus, without limit we can't put any step forward. Limit of any function can be defined as the behavior of the function near a particular input. Let’s a function f has the output f(x) to every input x and the function has limit k and an input m. If f(x) is close to k then f(x) is close to m. In simple words, we can say as f(x) moves closer to k x moves closer to m. and if we talk about infinity we know that it is impossible to reach there but we still try to reach it.

Limits at infinity are 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. We are here to discuss about the Left Hand Limit and Right Hand Limit. Both left hand limit and right hand limit are the output values of the given function when input value approaches to a definite value. If we calculate the limit from right side we always get the value in greater from and if we calculate the limit from left side we always get a lesser value so if we calculate the limit from right hand side and limit from right hand side then the value of right hand limit will always be greater than left hand limit. Now we will see some example for better understanding of left hand limit and right hand limit.

Example 1: Solve the given limit by
limx→3−h (2x−4/x+3)?
Solution: As we are seeing that x->3-h, so limit is decreasing so we can say that this is a left hand limit

Let x=3-h then as x->3 , h->0 so now we can replace x by 3-h

lim h->02(3-h)-4/3-h+3,

lim h->06-2h-4/6-h,

Put h=0,

6-4/6-0,

2/6,

1/3,

We will solve the same example with the help of right hand limit we will just change the sign of limit from minus to plus.

limx→3+h (2x−4/x+3)
Solution: As we are seeing that x->3+h, so limit is increasing so we can say that this is a right hand limit

let x=3+h then as x->3 , h->0 so now we can replace x by 3+h

lim h->02(3+h)-4/3+h+3,

lim h->06+2h-4/6+h,

put h=0,

6-4/6-0,

2/6,

1/3.

As we are seeing that we are getting the same values from both the limits but in actual the value of right hand limit will always we greater than left hand limit value.

In this way we can calculate left and right hand limit in this we need to check for what values of x, h approaches to zero, then just put the value of x in terms of h and solve the given limit by putting h is equal to zero. This is all about left and right hand limit.