Question

Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sin 3x, x 0, = 0

Answer 1

To graph sin(3x), just sub in a set of values, maybe \({0,\pi/4, \pi/2,3\pi/4,\pi, 5\pi/4,6\pi/4,7\pi/4,2\pi}\) These values will be the x coordinates and the answer you get when you sub in will be the y coordinates.
To get the linear approximation to a sin function around 0 you can use a maclaurin expansion. It's already here: http://answers.yahoo.com/question/index?qid=20120301225911AAQUapm

graph it by subbing in the same values as you did for sin(3x)