Getting Started With Python an Assignment¶
Taxes¶
U.S. uses a progressive tax system. Using the 2023 data provided below, write a function that will compute the total tax properly.
Lists¶
Perhaps the greatest strength of python is iterating over lists. Use the difference formula of calculus to show that the derivative of \(\ln x\) at 1 is 1.
In other words show that as \(h\) gets smaller and smaller \(\frac{\ln(1+h)-\ln(1)}h\) approaches 1. Mathematically we write this as $\( \lim_{h\to 0} \frac{\ln(1+h)-\ln(1)}h = 1 \)$
Use the list provided below.
Extra challenge: Use the sympy package to compute the limit and derivative.
h = [1,0.1,0.001,0.002,0.0001,0.0000000001]
Truth of Summation¶
Verify the following summation formula using python for all \(n\) where \(n\in\mathbb{Z}\) and \(n\leq 1000\).
Extra challenge: Reduce the output to a single true or false. Do not attempt until original has been verified with a clean code.