Consider the function f defined by
f(x)= sin x/x, x cannot equal 0
1, x cannot equal 0
a) At what points does the graph cross the X-axis?
b) What is the relation between f(x) and tan x at points x cannot equal 0 at which f(x)=0?
c) What is the behavior of f as the absolute value of x approaches +infinity?
d) Sketch the graph of f(x).
Calculus - MathMate, Monday, December 13, 2010 at 6:56pm
By taking the limit as x->0,
lim x->0 f(x)=1
a. Everywhere else, f(x)=0 when sin(x)=0.
b. Since tan(x)=sin(x)/cos(x), so f(x)=tan(x)=0 whenever sin(x)=0, or x=kπ, except x=0.
c. As x->∞, f(x)=1/∞=0