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pp:2023:haskell:l08_2 [2023/04/27 13:48]
george.vanuta 		pp:2023:haskell:l08_2 [2023/04/27 14:16] (current)
george.vanuta
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 </​code>​ </​code>​
  
-**8.3.2.** In order to view an **infinite tree**, we need to convert it to a finite **binary tree**. Define the ''​sliceTree'',​ which takes a level ''​k'',​ an **infinite tree** and returns the first ''​k''​ levels of our tree, in the form of a finite one.+**8.3.2.** In order to view an **infinite tree**, we need to convert it to a finite **binary tree**. Define the function ​''​sliceTree'',​ which takes a level ''​k'',​ an **infinite tree** and returns the first ''​k''​ levels of our tree, in the form of a finite one.
  
 <code haskell> <code haskell>
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 **8.3.3.** Define the ''​generateTree''​ function, which takes a **root** ''​k'',​ a **left generator** function ''​leftF''​ and a **right generator** function ''​rightF''​.\\ **8.3.3.** Define the ''​generateTree''​ function, which takes a **root** ''​k'',​ a **left generator** function ''​leftF''​ and a **right generator** function ''​rightF''​.\\
-For example, let's say we have ''​k=2'',​ ''​leftF=(+1)'',​ ''​rightF=(*2)''​. This should generate a tree where the root is $math[2], the left child is $math[parent + 1]\\ +For example, let's say we have ''​k=2'',​ ''​leftF=(+1)'',​ ''​rightF=(*2)''​. This should generate a tree where the //root// is $math[2], the //left child// is $math[parent + 1]\\ 
-and the right child is $math[parent * 2].+and the //right child// is $math[parent * 2].
  
 <code haskell> <code haskell>
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 derivativeApprox :: (Double -> Double) -> Double -> Double derivativeApprox :: (Double -> Double) -> Double -> Double
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-</​code>​ 
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-==== The Newton-Raphson Method ==== 
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-**8.4.8.** ​ 
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-The method used for approximating the square root is derived from a more general one, named **The Newton-Raphson Method**. 
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-This is a generic method used for finding the **roots** of a function ($math[x] | $math[f(x) = 0]). 
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-Considering the following //​sequence//:​ 
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-$math[x_{n+1} = x_n - \frac{f(x_n)}{f'​(x_n)}] 
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-and the //limit//: 
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-$math[\displaystyle \lim_{n \rightarrow \infty} x_n = r\ \Rightarrow \ f(r) = 0] 
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-write a function which takes another ''​function''​ and it approximates a root with **tolerance** ''​e=0.00001''​. Make use of ''​build'',​ ''​select''​ and ''​derivativeApprox''​. 
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-<code haskell> 
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-rootApprox :: (Double -> Double) -> Double 
  
 </​code>​ </​code>​