The objective of this problem is to compare second-order accurate forward, backward, and centered finite-difference approximations of the first derivative of a function to the actual value of the derivative. this will be done for
f (x) = e−2x − x
(a) use calculus to determine the correct value of the de­rivative at x = 2.
(b) develop an m-file function to evaluate the centered finite-difference approximations, starting with x = 0.5. thus, for the first evaluation, the x values for the cen­tered difference approximation will be x = 2 ± 0.5 or x = 1.5 and 2.5. then, decrease in increments of 0.1 down to a minimum value of δx = 0.01.
(c) repeat part (b) for the second-order forward and back­ward differences. (note that these can be done at the same time that the centered difference is computed in the loop.)
(d) plot the results of (b) and (c) versus x. include the exact result on the plot for comparison.

We as humans write math expression in infix notation, e.g. 5 + 2 (the operators are written in-between the operands). in a computer’s language, however, it is preferred to have the operators on the right side of the operands, i.e. 5 2 +. for more complex expressions that include parenthesis and multiple operators, a compiler has to convert the expression into postfix first and then evaluate the resulting postfix.write a program that takes an “infix” expression as input, uses stacks to convert it into postfix expression, and finally evaluates it. it must support the following operations: + - / * ^ % (example infix expression: (7 - 3) / (2 + 2)postfix expression: 7 3 - 2 2 + /result: 1guidelines: 1. you will need to use stacks in three placesa. one for the parenthesis check [char stack]b. one during infix to postfix [char stack]c. one during evaluation [int stack]for a and b above, you can use same array and same push, pop method as both ofthem are char. but for evaluation you have int stack and you might consider to createanother push pop method to handle it. maybe push_int, pop_int, etc. or find otherstrategy to utilize existing push pop method2. you can create a function for obtaining operator priority. that function should take anoperator as input and return its priority as an integer. this function will you a lot andreduce repeated code3. during evaluation you will need to convert char into integer. example for single digit: char c = '5'; int x = c - '0';

Working on this program in python 3.7: a year in the modern gregorian calendar consists of 365 days. in reality, the earth takes longer to rotate around the sun. to account for the difference in time, every 4 years, a leap year takes place. a leap year is when a year has 366 days: an extra day, february 29th. the requirements for a given year to be a leap year are: 1) the year must be divisible by 42) if the year is a century year (1700, 1800, the year must be evenly divisible by 400some example leap years are 1600, 1712, and 2016.write a program that takes in a year and determines whether that year is a leap year.ex: if the input is 1712, the output is: 1712 is a leap year. ex: if the input is 1913, the output is: 1913 is not a leap year. your program must define and call the function isleapyear(useryear). the function should return true if the input year is a leap year and false otherwise.

Which one of the following is the most accurate definition of technology? a electronic tools that improve functionality b electronic tools that provide entertainment or practical value c any type of tool that serves a practical function d any type of tool that enhances communication