Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Limit and Functions

Tere is a question consider a function f (x)=3+x we we give it 2 it become 5       and limit    x approach 2 it also become 5 why we put 2 in both is both are same limit and function what we think about limit

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: Limit and Functions

hi Zeeshan 01

Limits are used to show what a sequence of function calculations comes to as 'x' approaches a particular value.  So for f(x) = 3 + x and x approaching 2 we might try:

f(1.9) = 3 + 1.9 = 4.9
f(1.99) = 3 + 1.99 = 4.99
f(1.999) = 3 + 1.999 = 4.999

and so on.

You can see that as x gets closer to 2, f gets closer to 5.

The same limits applies if x approaches 2 from above:

f(2.1) = 3 + 2.1 = 5.1
f(2.01) = 3 + 2.01 = 5.01
f(2.001) = 3 + 2.001 = 5.001

With your example anyone can calculate f when x = 2 anyway, so there is nothing remarkable about the limit.

But sometimes it is not possible to calculate a function at a certain value eg.  f(x) = tan(x) where x is measured in degrees cannot be evaluated at x = 90.

By trying 89.9, 89.99, 89.999 and so on you will discover that the limit is infinity.

But try 90.1, 90.01, 90.001 etc and you will find the limit is minus infinity.  So left and right limits are not always the same.

There's a starter page on limits here: http://www.mathsisfun.com/calculus/limits.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob