Solution to Exercise 1.36:

`(define tolerance 0.00001)`

(define (fixed-point f first-guess)

(define (close-enough? v1 v2)

(< (abs (- v1 v2)) tolerance))

(define (try guess)

(display guess)

(newline)

(let ((next (f guess)))

(if (close-enough? guess next)

next

(try next))))

(try first-guess))

```
```(define (average a b) (/ (+ a b) 2))

(define result-with-damping

(fixed-point (lambda (x) (average x (/ (log 1000) (log x))))

2.0))

(display "result-with-damping: ")

(display result-with-damping)

(newline)

(newline)

(define result-without-damping

(fixed-point (lambda (x) (/ (log 1000) (log x)))

2.0))

`(display "result-without-damping: ")`

(display result-without-damping)

Output:

`2.0`

5.9828921423310435

4.922168721308343

4.628224318195455

4.568346513136242

4.5577305909237005

4.555909809045131

4.555599411610624

4.5555465521473675

result-with-damping: 4.555537551999825

```
```

`2.0`

9.965784284662087

3.004472209841214

6.279195757507157

3.759850702401539

5.215843784925895

4.182207192401397

4.8277650983445906

4.387593384662677

4.671250085763899

4.481403616895052

4.6053657460929

4.5230849678718865

4.577114682047341

4.541382480151454

4.564903245230833

4.549372679303342

4.559606491913287

4.552853875788271

4.557305529748263

4.554369064436181

4.556305311532999

4.555028263573554

4.555870396702851

4.555315001192079

4.5556812635433275

4.555439715736846

4.555599009998291

4.555493957531389

4.555563237292884

4.555517548417651

4.555547679306398

4.555527808516254

4.555540912917957

result-without-damping: 4.555532270803653