Posted by **Nikki** on Monday, December 13, 2010 at 4:40pm.

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
f(x)=sin(x)/x

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

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