PAPER Topics

Start of Term Paper
It is incredible how far calculators have come since my parents were in college, which was when the square root key came out. Calculators since then have evolved into machines that can take natural logarithms, sines, cosines, arcsines, and so ....

Middle of Term Paper
... arithmetic operators. So how do mathematicians take a function and turn it into a polynomial function? Lets find out. First, lets assume that we have a function in the form y= f(x) that looks like the graph below. We'll start out trying to approximate function values near x=0. To do this we start out using the lowest order polynomial, f0(x)=a0, that passes through the y-intercept of the graph (0,f(0)). So f(0)=ao. Next, we see that the graph of f1(x)= a0 + a1x will also pass through x= 0, and will have the same slope as f(x) if we let a0=f1(0). Now, if we want to get a better polynomial approximation for this function, which w ...