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

## Answer This Question

## Related Questions

- Calculus - Let f be a twice-differentiable function defined on the interval -1.2...
- Calculus c - Let f be a twice-differentiable function defined on the interval -1...
- math - indicates required items An operation * is defined by the relation x*y = ...
- Calculus - Functions? - #1. A cubic polynomial function f is defined by f(x) = ...
- Calculus - Consider the function x^2+x-4 Estimate the area between the graph and...
- Calculus - Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x...
- Calculus - Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x...
- calculus - a solid lies between planes perpendicular to x-axis at x=0 and x=17,...
- calculus - The graph of f'(x) is shown for 0=< x =<10. The areas of the ...
- Calculus - 4) f(x)= { 3x^2 x< and equal 1 { ax+ b x > 1 What is the ...

More Related Questions