Write a Lisp Program to Compute the Series - Mathematics Assignment Help

Assignment Task:

Task:

Question 6 (20 pts)  
Write a lisp program to compute the series for the sin(x) and cos(x) depending on the value of n. The function takes 2 arguments (x and n) and based on the value of n calculates one of the following functions: 
sin-cos-comp (x, n) 
{ 
sin(x) . x _ x3 + x5 x7 xn 31 5T. — T j_ -1- • • • +  n! 
, xn 4V*** -1- 771 cos(x) . 1 _ c! + x4! — x6 + 
-10 <x <10,n is odd 
n is even 
You are not allowed to use any inbuilt functions except predicate functions to check value type. Your program should print an appropriate message for string and decimal values for n. Additionally, there is a limit for x when n is an odd number. 
Question 7 (20 pts) 
In mathematics, the Pell numbers are an infinite sequence of integers, that comprises the denominators of the closest rational approximation to the square root of 2. The sequence of approximations begins with .... 
1 3 7 17 41 1 2 5 12 29 
So the sequence of Pell numbers begin with 1, 2, 5, 12, 29,..... The Pell numbers are defines as follow: 0 if n = 0 Pn = 1 if n = 1 2Pn-i + Pn-2 
otherwise 
Writ a lisp program that computes the Pell numbers for an input argument n using: 
a) An iterative approach b) A recursive approach 
For example pellnumbers (6 ) should return a list (0 1 2 5 12 29 70) 
Write at least 2 test cases for each version (a and b). 
 

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