### Section 1.3.2 - Constructing Procedures Using Lambda

#### Exercise 1.34

It will blow up trying to use the number 2 in the function position. Observe:

### Section 1.3.3 - Procedures as General Methods

#### Exercise 1.35

We already know that:

\[\phi^2 = \phi + 1\]
and dividing both parts by \(2\):

\[\phi = 1 + \frac{1}{\phi}\]
So:

#### Exercise 1.36

Here is `fixed-point`

now:

And we can define \(x^x\) as:

Now we can call both:

34 steps. Now with dampening:

13 steps. Dampening helps a lot in this case.

#### Exercise 1.37

We can define `cont-frac`

as such:

It takes 11 iterations to reach four-digit accuracy:

This was of course a recursive process. We can write an iterative now:

Note that the iterative solution has to calculate the result from the ground up,
starting from \(k\) all the way up to \(1\).

#### Exercise 1.38

We need to define `d`

:

For \(k = 8\) the approximation is accurate to 4 decimal places.

#### Exercise 1.39

Again, using `cont-frac`

: