This is a multiple choice question from my homework. The problem is:
f(x) =Sin x / absolute value x
Graph the following function to see whether it appears to have a continuous extension to the origin.
Can it be extended to be continuous at the origin from the right or left?
(This I can do without a problem) but...
The CORRECT ANSWER according to the book is...
The function cannot be extended to be continuous at x=0. It can be extended to be continuous at the origin from the right if f(0)=1, or from the left if f(0)=-1.
So is the book wrong? The function never intersects the origin.
Are they saying the origin isn't necessarily (0,0)?
Are they saying if f(0)=1, then the line is continuous at the origin because both points
(0,1) (from the right)
(3,0)
or
(0,-1) (from the left)
(-3,0)
both the x axis and the y axis intersects are continuous, although not at the origin, but this constitutes the line being continuous at the origin?
f(x) =Sin x / absolute value x
Graph the following function to see whether it appears to have a continuous extension to the origin.
Can it be extended to be continuous at the origin from the right or left?
(This I can do without a problem) but...
The CORRECT ANSWER according to the book is...
The function cannot be extended to be continuous at x=0. It can be extended to be continuous at the origin from the right if f(0)=1, or from the left if f(0)=-1.
So is the book wrong? The function never intersects the origin.
Are they saying the origin isn't necessarily (0,0)?
Are they saying if f(0)=1, then the line is continuous at the origin because both points
(0,1) (from the right)
(3,0)
or
(0,-1) (from the left)
(-3,0)
both the x axis and the y axis intersects are continuous, although not at the origin, but this constitutes the line being continuous at the origin?