Calculus
posted by Nikki .
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 Xaxis?
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).

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
Respond to this Question
Similar Questions

Calculus
4) f(x)= { 3x^2 x< and equal 1 { ax+ b x > 1 What is the relation between a and b if the function is continuous for allof x. 
math
indicates required items An operation * is defined by the relation x*y = 5x + 3y – 4xy. Evaluate [2*(1) ] A. 15 B. 10 C. 8 D. 3 A B C D An operation * is defined by the relation x*y = 5x + 3y – 4xy. Evaluate (3*2)*4 A. 15 B. … 
Calculus  Functions?
#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point of inflection at x= 2 a.) Find the values of a … 
calculus
The graph of f'(x) is shown for 0=< x =<10. The areas of the regions between the graph of f' and the xaxis are 20, 6, and 4, respectively. I'm going to describe the graph of f' since I can't post pictures. The first section … 
calculus
a solid lies between planes perpendicular to xaxis at x=0 and x=17,cross section perpendicular to axis interval 17 greater or equal x & x greater or equal 0 are squares of diagonals go from parabolas y=2x^(0.5) & y=2x^(0.5). find … 
Calculus
Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x))^2 at which the tangent line is horizontal. Consider the domain x = [0,2π). 
Calculus
Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x))^2 at which the tangent line is horizontal. Consider the domain x = [0,2π). Please help! 
Calculus c
Let f be a twicedifferentiable function defined on the interval 1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the xaxis at … 
Calculus
Let f be a twicedifferentiable function defined on the interval 1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the xaxis at … 
Calculus
Consider the function x^2+x4 Estimate the area between the graph and the xaxis between x=2 and x=4 using four rectangles and right end points.