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Exercise 1.11 A function f is defined by the rule that f(n) = n if n<3 and f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) if n> 3. Write a procedure that computes f by means of a recursive process. Write a procedure that computes f by means of an iterative process.

See ex-1.11.rkt

Exercise 1.15. The sine of an angle (specified in radians) can be computed by making use of the approximation sin x = x if x is sufficiently small, and the trigonometric identity

See https://codology.net/post/sicp-solution-exercise-1-15/

Exercise 1.16. Design a procedure that evolves an iterative exponentiation process that uses successive squaring and uses a logarithmic number of steps, as does fast-expt.

See https://codology.net/post/sicp-solution-exercise-1-16/

Exercise 1.17

See https://codology.net/post/sicp-solution-exercise-1-17/

aula

1. Procedimentos são abstrações que descrevem operações compostas!

(define (cube x) (* x x x))

1. Often the same programming pattern will be used with a number of different procedures. To express such patterns as concepts, we will need to construct procedures that can accept procedures as arguments or return procedures as values.
2. Procedures that manipulate procedures are called higher-order procedures.
3. Procedures as arguments

#lang racket

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
         (sum term (next a) next b))))

(define (identity n) n)
(define (inc n) (+ n 1))

(define (sum-integers a b)
  (sum identity a inc b))

(define (cube n) (* n n n))
(define (sum-cubes a b)
  (sum cube a inc b))


(define (pi-sum a b)
  (define (pi-term a)
    (/ 1.0 (* a (+ a 2))))
  (define (pi-next a)
     (+ a 4)) 
  (sum pi-term a pi-next b))


(define (integral f a b dx)
  (define (add-dx x) (+ x dx))
  (* (sum f (+ a (/ dx 2.0)) add-dx b)
     dx))

(integral cube 0 1 0.01)

Exercise 1.32

1. Constructing Procedures Using Lambda
2. Using let to create local variables

let ~ lambda

Exercise 1.34

1. Finding roots of equations by the half-interval method
2. Finding fixed points of functions
3. Procedures as Returned Values