LAB Topic 1 F23

Lab: Topic 1 will introduce how limits can be calculated numerically and provide additional practice creating computational Python programs. Certain functions are difficult to evaluate at particular values, where infinity or division by zero are involved, but can be understood by evaluating them at a number of values that approach zero or infinity. You are to write a program that produces several evaluations for one function. You should perform these evaluations by creating a sequence of print statements that output the desired numbers. Write a program named follow_directions.py that performs the following tasks for the function f ( x ) = sin ( x − 1 ) / ( x − 1 ) evaluated close to x = 1 . Use values of x ranging from 1.1 to 1.00000001 by inserting another zero after the decimal of the previous value ( x = 1.1 , x = 1.01 , x = 1.001 …). 1) First, print a line of text stating the purpose of the program 2) Next, print a line of text stating your guess for the final calculated value a. There are no wrong answers, just make a guess b. Think about the answer then see if your guess was close 3) Next, print out a sequence of 8 numbers, representing evaluating the function at 8 different values of x 4) Finally, print one blank line, followed by a statement of how good your guess is As an example, for the equation f ( x ) = tan ( x ) / x evaluated close to x = 0 , your output would look like what’s shown below. Make sure your code evaluates f ( x ) = sin ( x − 1 ) / ( x − 1 ) . Example output (using tan ( x ) / x ): This shows the evaluation of tan(x)/x evaluated close to x=0 My guess is 2 1.5574077246549023 1.0033467208545055 1.0000333346667207 1.0000003333334668 1.0000000033333334 1.0000000000333333 1.0000000000003333 1.0000000000000033 My guess was a little off Based upon Dr. Keyser’s Original 3 Revised Fall 2023 SNR