precalculus 2

2 ) Application of polynomials. We will study polynomials some more this 2nd week of the quarter. We've discovered through graphing various polynomials on Desmos that the graphs of polynomials are continuous smooth curves with no sharp corners or holes. AND polynomials end up being very easy functions to work with in Calculus and beyond. So nice, that we tend to approximate difficult functions using polynomials. For example, your calculator uses polynomials to approximate trigonometric functions (sin x, cos x, tan x, ... Math 48C stuff next quarter). x 7 (-1) * x2k+1 sin x ~ x 3 ! 5 ! 7 ! 9 ! (2k + 1)! The function on the left is the sine function. The function on the right is actually a polynomial (a bunch of terms being added/subtracted with whole number exponents on the variable x and the coefficient of each term is a real number, right?). Refer to page 8 of the posted lecture notes for Section 3.2, part 1 (posted on Day 2 of lecture notes, in the top Module of Canvas, titled Essentials). The lecture notes explains what the exclamation mark, ! , actually means in math. It's called a factorial. a) Use Demos to graph the function y = sinx. b ) In the second entry of Desmos, have it graph the polynomial on the right that involves factorials. What do you notice is happening to the graph of the polynomial as you type in more and more terms using the pattern you see? Explain in words and provide a sketch of both graphs to support your answer. That's it. Hope you found this activity interesting