3. Write a function TrapezoidalRule.m which takes three input arguments f, a and b and returns one output argument I. You must use a for loop to compute the trapezoidal rule approximation to the integral 1 = = b-a N-1 Use the definition line function [I] = The input arguments mus where h = N-1 +fN [ f(x)dx = n(f₁ + fx + [fu) h 2 k=2 zoidalRule(f,a,b) 1 x N array f scalar (1 x 1 array) a and b scalar (1 x 1 array) I Test your function with f= [0:0.1:2].^3, a-0, b-2 which should give I = 4.01000. must be auffal The output argument must be
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- Your task is to complete a function GetArrangements() that returns the count of all the possible arrangements of length N that can be derived from the characters of an input string of length N. The input string may or may not have repeated characters. Your function should handle all the possible cases. For example,for the input provided as follows:ABCBThe function should return12Write a function that adds two polynomials. Ensure that the polynomial produced matches the requirements in HASKELL. addPoly :: (Num a, Eq a) => Poly a -> Poly a -> Poly a For example: > addPoly (P [1]) (P [-1,1])P [0,1]> addPoly (P [17]) (P [0,0,0,1])P [17,0,0,1]>addPoly (P [1,-1]) (P [0,1])P [1] You may find it helpful to write addPoly using two helper functions: one to combine the lists of coefficients, and one to trim trailing zeroes.MAKE A FLOWCHART PLEASE clc;clear; function [] = Bisection(xl,xu,es,imax)ea = 100xr = (xu+xl)/2;x=xrfr=evstr(f)while (ea>es)a=fl-fu;if (a==0) thenmprintf("Error: Division by Zero")abortendtest = fl * fr;mprintf(" %d %10f %10f %10f %12.7f %12f %12.f %10.7f\n",iter,xl,xu,xr,fl,fu,fr,ea);if (test<0) thenxu=xr;elseif (test>0) thenxl=xr;elseif (test==0) thenmprintf("\n\nThe root of the equation is %f",xr)abortendx=xlfl=evstr(f)x=xufu=evstr(f)xrold=xrxr=(xu+xl)/2;x=xrfr=evstr(f)ea=abs((xr-xrold)/xr)*100;iter=iter+1;test=fl*frif ea < es thenmprintf(" %d %10f %10f %10f %12.7f %12.f %12.f %10.7f\n",iter,xl,xu,xr,fl,fu,fr,ea);mprintf("\n\nThe approximate root for the given function is %f",xr)abortendif iter > imaxmprintf("The approximate root for the given function is %f",xrold)mprintf("\nSlowly converges. It is suggested that the initial values should be change");abortendendendfunction //main disp("This program will solve/give the approximate root of any given nonlinear…
- In Kotlin, Write a function that uses you work from the last two questions to identify all the Pythagorean triples whose sides and hypotenuse lengths are all integers between 1 and 20.Define a function which takes one parameter N, and use loop(s) to control and output a pyramid pattern as follows: print a total of N rows, the number of asterisks in each row equals the row number (e.g. the 1st row has 1 asteroid, the Nth row has N asteroids). Note the pattern should be center aligned. E.g. when N is 5, you will print the following pattern * * * * * * * * * * * * * * *Write a function that determines if two strings are anagrams. The functionshould not be case sensitive and should disregard any punctuation or spaces.Two strings are anagrams if the letters can be rearranged to form each other.For example, “Eleven plus two” is an anagram of “Twelve plus one”. Each stringcontains one “v”, three “e’s”, two “l’s”, etc. Test your function with severalstrings that are anagrams and non-anagrams. You may use either the string classor a C-style string. use c++
- Define a function CalcPyramidVolume with double data type parameters baseLength, baseWidth, and pyramidHeight, that returns as a double the volume of a pyramid with a rectangular base. Relevant geometry equations:Volume = base area x height x 1/3Base area = base length x base width.(Watch out for integer division). 419894.2696446.qx3zqy7 #include <iostream>using namespace std; /* Your solution goes here */ int main() { double userLength; double userWidth; double userHeight; cin >> userLength; cin >> userWidth; cin >> userHeight; cout << "Volume: " << CalcPyramidVolume(userLength, userWidth, userHeight) << endl; return 0;}4. Using c++ Write a function isPrime that accepts a positive long num and returns true IFF num is prime (e.g. only divisible by 1 and itself).Two numbers are said to be co‐prime, if the greatest common divisor of the numbers is one. Forexamples,13 and 14 are co‐prime but 14 and 21 are not.a. Write a C function gcd_helper (int x, int y) to find the greatest common divisor of twonumbers x and y.b. Write a C function CoPrime_helper (int a, int b) to test whether the pair of numbers aand b are co‐prime by using gcd_helper() function.In the main() function, read five numbers and use the CoPrime_helper ( ) function to test howmany pair of them are co‐prime.
- In C program Write a function bracket_ by_len that takes a word as an input argument and returns the word bracketed to indicate its length. Words less than five characters long are bracketed with << >> , words five to ten letters long are bracketed with (* *) , and words over ten characters long are bracketed with /+ +/ . Your function should require the calling function to provide as the first argument, space for the result, and as the third argument, the amount of space available. Consider the expected results of these calls to the function.For example:bracket_ by_len(tmp, "insufficiently", 20) "/+insufficiently+/"bracket_ by_len(tmp, "the", 20) "<<the>>"In Kotlin, write a higher-order function with an expression body that takes an int n and a function f from int to int and returns the result of calling f(f(n)). For example if you call the function with n = -5 anda function that calculates absolute value, your function will return 5, and if you send the value 2 and a function that calculates the sqaure of an int, the function will return 16. in addition to the function, write the syntax to call it with:a. a function name as the function arguementb. some lambda expression as the function argumentConsider the PreviousDate() function. This function takes three parameters month, date, and year as inputand returns the date of the day before. For example if the input is month = 4, day = 23, year = 1989, theoutput will be 22-04-1989 (or April 22, 1989). The 3 inputs are integer values and with followingconstraints:1 ≤ month ≤ 12, 1 ≤ day ≤ 31, 1712 ≤ year ≤ 2112Design test cases based on boundary value testing.