;;
(func f(x) x + sin x)
(plot f 0 2pi)

;; 9, of 5.7
(func f(x) ln x - 1 / x)
(newton-root f 1)
;; f switches sign between 1.76 and 1.77, so root has form 1.76....
(f 1.76)
(f 1.77)

;; 10, of 5.7
(func f(x) x ^ 2 - a)
(def a 2)
(def x0 (calc a / 2))
(newton-root f x0)
(f 1.4142)
(f 1.4143)

(def a 10)
(def x0 (calc a / 2))
(newton-root f x0)
(f 3.1622)
(f 3.1623)

(def a 1000)
(def x0 (calc a / 2))
(newton-root f x0)
(f 31.6227)
(f 31.6228)

(def a pi)
(def x0 (calc a / 2))
(newton-root f x0)
(f 1.7724)
(f 1.7725)