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We'll discuss here how to choose a sequence of functions converging to
a given function `f`. This discussion should make the
construction of the approximating sequence in the proof easier. But,
it will **not** give any indication of why the sequence of functions
is actually a polynomial. That is a very clever insight which you'll
see in the main proof.`g`_{n}(x) look like as
`n` increases?`f(n)`.`f(x) g`_{n}(x) and compare it with
the graphs of `g`_{n}(x) and `f(x)`. Judging by
the graph, what do you think
converges to?
`f`. Can we use this last observation to make some functions
that converge to `f(t)`?

Question: What does the graph of

Here is the graph of

Question: Sketch the graphs of

Question: Now, what we really want is to have a sequence of functions converging to