= P1*1 P2*₂. -Prk. et g = gcd(k₁, k2.... k) and m, = k₁/g. he function F is defined as: F(n) = P11 P22- Tow we have to summing up the value of this function for the first N natural r P.m
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- python this is connected to the last problem - the second part of the question is added. my attempt on this problem shows that the part b) (approaches N*NH) is not really wokring.. a) (answered) with a function “harmonic(n)” that computes the n-th harmonic number, write a function “harmonic_all(n)” that returns the number of values generated until all values are obtained as a function of the range of possible values n, then write a function “harmonic_sim(n)” that repeats “harmonic_all(n)” a total of n_sim = 100 times. (Attaching the code from the answer for a) d) Show that as n increases (e.g., with a doubling experiment), from n = 2 to n_max = 1,000, the value of “coupon_sim(n)” approaches “n * Hn”.Given a function f from {1, 2, … , n} to itself, using Python, write a program to determine whether f is onto.In C programming Mathematically, given a function f, we recursively define fk(n) as follows: if k = 1, f1(n) = f(n). Otherwise, for k > 1, fk(n) = f(fk-1(n)). Assume that there is an existing function f, which takes in a single integer and returns an integer. Write a recursive function fcomp, which takes in both n and k (k > 0), and returns fk(n). int f(int n);int fcomp(int n, int k){
- a) Implement a function start( ) that takes as input a positive number a, rounds its logarithm base 4 to the nearest integer n, and returns the value of 1.0 x 2^n.Write a python function sqr(n) that returns the square of its parameter n for example: Test Result print(sqr(-3)) 9 print(sqr(11)) 121Write a Python function for reading the data below and make the following plot. #Measurements of arbitrary quantity #(abscissa, ordinate) [xau x yau] n_pts = 26 -2.00 -9.37 -1.00 +10.00 -1.14 +10.83 -0.29 -13.88 +0.00 -18.00 +0.57 -1.83 +1.00 +14.00 +1.43 +14.5 +2.00 +0.00 +2.29 -1.38 +3.00 +28.00 +3.14 +35.64 +4.00 +37.88 +5.00 -23.00 +4.86 -17.52 +5.71 -14.63 +6.00 -1.00 +6.50 -15.00 +6.57 -1.73 +7.00 +12.00 +7.43 +5.97 +7.50 +2.00 +8.29 +22.78 +9.00 +1.00 +9.14 -6.41 +10.0 -9.37
- 3. Write a program to evaluate a polynomial \[ p(x)=c_{n} x^{n}+c_{n-1} x^{n-1}+\cdots+c_{2} x^{2}+c_{1} x+c_{0} \] and its derivative at a given pointt. The input is the row vectorcof coefficients of the polynomial arranged from highest to lowest power, and the numbert, and the two outputs arep(t)andp′(t). Computep(t)by first computing the row véctor \[ \left[t^{n}, t^{n-1}, \ldots, t^{2}, t, 1\right] \] and combine that with the vectorcto get the result. Computep′(t)by computing the coefficients of the derivative polynomial from the vectorc, and then evaluating that polynomial in the same way. Include some tests that provide evidence that your code produces the correct results. Please give proper explanation and typed answer only.Implement a C function, named triangle, that outputs Pascal’s triangle. In general, the Pascal’s triangle can be represented as: 0C0 1C1 1C0 2C2 2C1 2C0 3C3 3C2 3C1 3C0 4C4 4C3 4C2 4C1 4C0. . .where nCr represents how many ways there are to choose r from n, not counting duplicates. The formula used to calculate nCr can be written as:nCr = n!/r!(n −r)!where n! is the factorial of n. The function triangle:• is called by value where exactly one parameter (the number of rows of Pascal’s triangle)is passed to it.• returns void (i.e., no value).• prints out Pascal’s triangle to the standard output.• Employs two other functions, namely:– int choose(int n, int r);That chooses r from n– int factorial(int n);That calculates the factorial of n.Note: You are allowed — in fact, encouraged — to design and use any other functions as needed. Note:• The number of the rows is limited to integers between 0 and 13 inclusive.• If 0 is entered…In this question, we are going to write a Racket functionwordMaxIndex that calculates the maximum index of each word thatappears in an input word list. For example, if the input is’(time is long but life is short)Then one output can be((time 0) (long 2) (but 3) (life 4) (is 5) (short 6))The index of the first word in a word list is 0; the index for the secondword is 1; etc. Therefore, in the previous example, the maximum indexfor word “time” is 0; the maximum index for word “is” is 5, since “is”appears twice, at index 1 and 5. Note that you are not asked to sortthe words in the output. Therefore, the output is correct as long asthe indexes are correct.Do the following steps to implement the word-index program. In ourdiscussion, we call a word with an index a word-index pair, for example,(short 6) and (is 5) are word-index pairs. We call a list of word-index pairs a word-index list.(a) Write a function initialWIList that takes a list ofwords and creates a word-index list. The resulting…
- Write a program in Python with a function squareRoot(x, epsilon) that uses bisection search to return a number y that is close enough to the square root of x, so that abs(y**2 - x) < epsilon.Using a pseudo random number generation function (e.g., rand() in C or other equivalentfunctions in other languages) that generates uniformly distributed random numbers,write functions that generate the following:(a) uniformly distributed integers between 0 and 99. (b) uniformly distributed floating numbers between 0.25 and 0.5. (c) the number 1 with probability 0.5, the number 2 with probability 0.2, otherwise a floatuniformly distributed between 3 and 4.Write a C program that reads two matrices of integers. It then generates the sum and difference of the two matrices. The sum of the two matrices of the same size is a matrix with elements that are the sums of the corresponding elements of the two given matrices. Addition is not defined for matrices of different sizes. If A and B are matrices of the same size, then we define subtraction as follows: A – B = A + (-B). Thus, to subtract matrix B from matrix A, we simply subtract corresponding elements.
