All the questions below are examples that use a "While loop" How to assure proper input Question Using a while loop to ask the user to input a number between 1 and 10 (inclusive) Question Repeated Menu Another common use of while loops is to allow a user to repetitively make choices from a menu and act on them. While loops that terminate on a specific value are commonly called sentinel controlled loops. A sentinel is an indicator of some condition being met and a sentinel controlled loop usually repeatedly reads in values and tests them until the sentinel input is detected. The first input is typically read in before entering the sentinel controlled loop. The menu is displayed and the first choice read in from the user. This is the initialization; the variable choice is used in the loop logical expression The loop body is executed as long as the choice is not quit. The loop body will not be executed if the user chooses the quit choice initially. In the loop body, the selected function is evaluated and plotted. The menu is then displayed and the next choice read in from the user. The variable in the loop logical expression is modified with the new value read in so the loop can terminate when the choice is quit. Question Approximating a Taylor Series The Teylor series of a real valued for complex valued function that is infinitely differentiable a valve als (--) Where it is the factorial of kand") is the kth derivative (1) with respect to evaluated atxa. The Taylor series for the function(x) == I! 2134 The program below approximates the function f(x) = e "at a=0 to an accuracy of t = 0.00001, .i.e. the error bound is E.(x)0.00001 To approximate a function to a set accuracy using a Taylor polynomial. the value of n is not known beforehand so the program of below uses a while loop to perform a running sum of the terms of the Taylor polynomial until the error bound is met. To determine the error bound. the (n+1)st derivative of the function is needed. In practice, if we are approximating a function using a Taylor polynomial, the (n+1 )st derivative of the function is not known and so the error bound must be estimated Question Write a MATLAB program that will sum positive numbers (numbers greater than or equal to zero) read in from the user until the value -999 is entered. Once the value_999 is entered the sum of the all the positive Question Write a MATLAB program that will sum positive numbers (numbers greater than or equal to zero) read in from the user until the value -999 is entered. Once the value-999 is entered, the sum of the all the positive numbers previously entered should be displayed. Hint: this is a running sum problem but you should use a while-loop since you do not know how many numbers will be entered. The sentinel value (the value -999 that indicates the end) should not be added to the sum. Use the comment skeleton of the Figure below as a starting point Question Create a MATLAB Script File to calculate and plot the value of y for 5
