1.The standard Python function sum takes a list as argument and computes the sum of the elements in the list. Write your own version 'mysum()' which · accepts a container as a single argument (list,...

python 3 codes are required


1.The standard Python function sum takes a list as argument and computes the sum of the elements in the list. Write your own version 'mysum()' which · accepts a container as a single argument (list, dictionary, tuple, set) and · returns the sum of the elements as a single number. · No testing for non-numeric data is required. You might need to treat different types of containers differently. 2. The mathematician Ramanujan found an infinite series that can be used to generate a numerical approximation of ππ: 1/π=(2sqrt(2)/9801)*∑00k=0 ((4k)!(1103+26390k))/((k!)4 *3964k ) . Write a function called 'estimate_pi()' that · takes no input argument · uses the formula above to compute an estimate of ππ. · Return your result, noting that a manual return value of ππ (math.pi or 3.1415...) will be moderated to zero marks. · Use a 'while' loop to compute terms of the summation until the last term is smaller than 1.0e-15 (i.e. 10-15). · Note that you'll either have to use a built-in factorial function or use your own from earlier exercises in the script. 3. Write a function 'mean_rms_file()' which · receives as single input argument a file name as a string. · The function shall open the file and · read the single-column data and · calculate the mean value of the numbers in the file as well as the RMS (root mean square) value, see below. · You can test your function with Spyder using the supplied 'data1.txt' file (Result: mean =20.95=20.95, RMS =21.1569=21.1569...). · Return the mean value and the RMS value as a tuple in that order. Note that the RMS value is defined as XRMS=sqrt(σ2+xmean) where σ2 is the variance of the data, xmean the mean value. 4. A ball thrown at an angle θθ with initial speed v0v0 on Earth follows a trajectory f(x)=xtanθ−1/(2*v02 )*g*x2 /(cos2(x))+y0 where g=9.81 ms-2, speed in units of ms-1 and an initial height y0y0 in metres. Set y0=0  and write a function 'trajectory()' that · has three input variables: xdata (a list), speed and angle (constant numbers each, angle in degrees) in that order. · Return the calculated list of height values, f(x), containing only positive or zero values for the ball height, i.e. remove all negative values before returning the resulting list. · The moodleX test code will take the returned list and test maximum height at given speed and angle. You can test your function with Spyder by writing a test function, calling your trajectory function with a speed of 20 ms-1−1, an angle of 45 degrees and a list made from the python function 'range(100)'. Printing the maximum of the list with 'max(result)' where result is the output of the trajectory function should yield 10.19 in this example.