Will we hate maths if we learn this way?

1. An example for Limits
Many people hate mathematics, because they are not taught mathematics properly.
Now let us look at one of the simplest concepts of Limits in Calculus.
The topic of limits is one of the most important topics in calculus.
Unfortunately most people who take calculus often confuse the fundamental concept
of a limit.
The symbols “
)(lim xf
ax→
” mean as x gets closer to “a” what is f(x) getting
closer to, NOT what f(x) is at a.
This is mainly because most of the texts on Calculus start as under
lim ( 2x2
+4) = 4
X 0
we substitute the value of x =0and calculate the value of the function.
I think it is essential that we should be able to give a good example to
illustrate the concept of limit namely
When we say that t X 0, it means that the value of X tends to be 0 but it
will never be 0.
To have a conceptual view of this let us take 95 ml of water and add to 5
grams of sugar( or salt). Let us assume for our convenience 5 gram of sugar (salt) =
5 ml. Then now we have 100 ml of sugar (salt ) solution
Where the sugar(salt ) is 5/100 = 0.05
Now let us add 900 ml of water to this solution. With this we get I liter of
Sugar(salt) solution. The amount of sugar (salt) now is 0.005.
Let us now add 9 liters, 90 litres,900 liters etc of water, we will see that the
sugar(salt) present in the solution goes further down to 0.0005 to 0.00005, 0.000005
etc.,
Now let us imagine that all the water available in the whole universe is
added to this solution and when we determine the amount of sugar or salt present
we can see that it is 0.0000...................................5.
You can see that the value approached to zero but it will never be zero.
I think the above example will help students to understand the concept of
Limit in a better way. Explanations in this manner on other concepts of mathematics
would make people love mathematics instead of hating it.
(This is from my forthcoming book on Operations Research( Quantitative Techniques
where I am attempting to do the same for Operations Research)
I would be grateful for your kind feedback
Dr. R.Ramakrishnan, Classic Consultants, Salem India
ramakrish54@gmail.com +919952669656