#$&*
mth173
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
Question: `q Query problem f(x) = sin(3x)/x.
Find the value of f(x) at x = -.1, -.01, -.001, -.0001 and at .1, .01, .001, .0001 and tell what you think the limit of this function, as x approaches zero, should be.
Your solution:
Confidence Assessment:
Given Solution:
COMMON ERROR: Here are my values for f(x):
-.1, 2.9552
-.01, 2.9996
-.001, 3
-.0001, 3
.1, 2.9552
.01, 2.9996
.001, 3
.0001, 3 .
So the limiting value is 3.
INSTRUCTOR COMMENT: Good results and your answer is correct. However none the values you quote should be exactly 3. You need to give enough significant figures that you can see the changes in the expressions.
The values for .1, .01, .001 and .0001 are 2.955202066, 2.999550020, 2.999995500, 2.999999954. Of course your calculator might not give you that much precision, but you can see the pattern to these values.
The limit in any case is indeed 3.
** **
You give the funtion f(x) = sin(3x)/x. and then ask us to Find the value of f(x) at x = -.1, -.01, -.001, -.0001 and at .1, .01, .001, .0001.
I understand what you are asking but when I attempt to work it out I do not get The values for .1, .01, .001 and .0001 are 2.955202066, 2.999550020, 2.999995500, 2.999999954.
I get .052359638,.052359875, .052359878, .052359878 for .1, .01, .001, .0001.
** **
@& You probably have your calculator in degree mode.
We don't do calculus in degree mode. That would lead to a big headache with the chain rule, as you'll see.
The natural unit to use for the angle in trig functions is the radian. Your calculator needs to be in radian mode.*@
@& The default unit of angle is the radian. If we intend angles in degrees, we have to specify the unit 'degree'. If no unit is included, the angle is in units of radians.*@