18. Write a function that computes the value of e which can be approximated using the fol- lowing expression: 2 + 21/11 + + 2! 3! 1 n! where n is a positive integer. Write a program that uses this formula to approximate the value of e.
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- (Numerical) Heron’s formula for the area, A, of a triangle with sides of length a, b, and c is A=s(sa)(sb)(sc) where s=(a+b+c)2 Write, test, and execute a function that accepts the values of a, b, and c as parameters from a calling function, and then calculates the values of sand[s(sa)(sb)(sc)]. If this quantity is positive, the function calculates A. If the quantity is negative, a, b, and c do not form a triangle, and the function should set A=1. The value of A should be returned by the function.Write the definition of a function that takes as input two decimal numbers and returns first number to the power of the second number plus second number to the power of the first number. (4)(Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.
- 8. Write a function which calculates the following expression for a given number of terms (N) and x, e.g., efunc(N,X) ( takes N and x as an input) x2 ex - 1+ 1 ! + ... 2! 3!Part 1: Write a function factorialFunc(n) that gets the positive integer n and calculates n! n! = n*(n-1)* (n-2)* (n-3) … * 3 * 2 * 1; Part 2: sin(x) can be approximately calculated using the following formula, where n! is factorial(n) – for example 3!=3*2*1 = 6 (the function in previous problem). The more terms we use in the series, the higher will be accuracy of the calculations. By using infinite terms in the series we will have the exact value. Write a program that gets x and calculates sin(x) using 5, 10, 20 terms, using C++Write a function that adds two numbers. You should not use+ or any arithmeticoperators.
- Using functions, write a program that will solve the problem: Create a program that will display the nth numbers in the Fibonacci series. The length of the series depends on the user's input. Use user-defined function and appropriate conditional and looping statements to solve the given problem.Write a function that determines if a number is prime. Use this function in a program that determines and prints all the prime numbers between 1 and 10,000. Do the required commented changes in the following program codeTranscribed Image Text About initial programming in python: Consider the series: 8. 1)" 1 = 1- 3 1 1 1 2n | 1 n=0 whose sum converges ton/4 That is: П lim s, = a) Write a function that, given n, calculates the sum of the series up to term n. b) Write a function that calculates the sum of the series with an error of less than O.01, that is, calculate the sum of the series series such that |Sn-N/4| < O. 01. Your function must also return the number of terms necessary to reach this error, that is, your function will return a tuple with the two calculated values. Important: It is mandatory to use the function defined in the previous item. Hint: math.fabs(number) returns the absolute value (module) of a number.
- Write a function averageDigits that computes the average of the digits of a 3-digit positive number in the range [100,999), Use the following function prototype: double averageDigits(int); For example, averageDigits(936) returns 6.0 ((9+3+6)/3). Write a test program that prompts the user to enter a 3-digit number, call the function averageDigits and print the result in the main program. The process is repeated if the user enters y to continue.python code Problem 7 Define a function named z and have it take 3 arguments: score , mu (sample mean) , sigma (standard deviation).. Return the calculated z-score. Use your z function on this data to show it works: You have a test score of 190. The test has a mean (μ) of 150 and a standard deviation (σ) of 25. Now define a function named std_error and have it take 2 arguments: sigma (standard deviation) , and n. Return the calculated standard error Use your std_error function (you can assume a sample size of 10) Print the answer rounded to the 2nd decimal place. (you can look up these formulas online)(2) The ceiling of a floating-point number x is the smallest integer that is still larger than or equal to x. Alternatively, the ceiling of a floating-point number x is what you get when you round x up to the nearest integer. For example, the ceiling of 2.1 is 3, the ceiling of 0.9 is 1, the ceiling of -4.5 is -4, etc. Write a function called ceiling (number) to compute the ceiling of a floating-point number (input argument) and returns one integer value. You may not use python's ceil() or floor() functions. Your function may use int() and/or float() functions, and your solution must use the floor division operator (i.e., '//").