Lullaby (Calculus) Lyrics

Hi

Our lecture today

Actually has us backtrack a little bit

To a concept

Which is actually

More fundamental

Than that of

Differentiability

It's a topic which is called

Continuous functions

In other words

Our lecture today

Is concerned with a topic called

Continuity

And actually

The topic of continuity

Had its roots

Way back

At the beginning of our course

When we first raised the question

Does the limit of f(x)

As x approach a

Equal f(a)

Remember

When we first started talking about the limit concept

Our intuitive approach was to say look-it

As gets x arbitrarily close to a

F(x) gets arbitrarily close to f(a)

And we saw

That this particular definition

Had a few

Loopholes in it

Even though intuitively

This is what we would have liked

And so

What I want to do today

Is to see what happens

If we can be sure

That the limit of f(x)

As x approaches a

Equals f(a)

What is implied

If this happens to be

A true statement

And my first claim is

Is that

It is

Implicitly implied

That f(a)

Must at least make sense

Otherwise we wouldn't have

Written it over here