1. Let

(a) Replace by

(b) Expand the result so becomes a polynomial in

(c) Replaceby

This way
is expressed in the form

(d) Express
into the form

(e) Can you find a bound for the function
when
is near
In other words, find a constant
which
depends on the coefficients
and find
such
that the inequality

holds for all
satisfying

(f) Find any
such that

for all
satisfying

Find any
such that

for all
satisfying

Find any
such that

for all
satisfying

(g) For any
find
such that

for all
satisfying

2. Let
Given
find
depending on
such that

for all
satisfying

3. Let
Find
such that

for all
satisfying

4. Let What is Show that the function is ``bounded away'' from near . This means: there exists and such that for all satisfying

5. If is bounded away from near show that remains bounded near there exists and such that for all x satisfying

6. Let
Given
find
depending on
such that

for
all
satisfying