Write a program that computes the value of the expression: \lim_{(x\rightarrow\infty)}(1 + \frac{1}{n})^nlim (x→[infinity]) (1+ n 1 ) n between certain values of n and then compare the values with e. For example, you can compute the values of the expression between: 100 and 10,000 with an increment of 100 or between 1,000 and 1,000,000 with an increment of 1,000. The program should accept as input: The start value for n The end value for n (Note: The increment value of 100 should be hardcoded in the program upon final submission.) The program should then output the value of the expression for each value of n in the specified range with a decimal precision of 8.

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Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."

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