Posted by **Abi** on Wednesday, February 9, 2011 at 10:05pm.

Consider the function f(x)=sin(5x)/x.

(a) Fill in the following table of values for f(x):

x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1

f(x)=

( I need the values of f(x) for each x)

(b) Based on your table of values, what would you expect the limit of f(x) as x approaches zero to be?

lim x->0 sin(5x)/x=________

(c) Graph the function to see if it is consistent with your answers to parts (a) and (b). By graphing, find an interval for x near zero such that the difference between your conjectured limit and the value of the function is less than 0.01. In other words, find a window of height 0.02 such that the graph exits the sides of the window and not the top or bottom. What is the window?

________<=x<=_____

______<=y<=_______

Note: You can earn partial credit on this problem.

- Calculus -
**MathMate**, Thursday, February 10, 2011 at 12:00am
This is an exploratory exercise.

If the results are simply supplied, you will not benefit from the learning experience.

Try to follow the instructions using a scientific calculator. Post again if you have difficulties.

- Calculus -
**Abi**, Thursday, February 10, 2011 at 12:12am
the values I got for f(x) were

4.9; 4.99; 4.999; 4.9999; 5.0001; 5.001; 5.01; 5.1

The two firsts and the two lasts values are not correct and I dont know why...

the limit is 5

also what i have for the other part is

-.00001<=x<= .00001

4.9999<=y<=5.0001

the values for y are wrong, I dont know why.....

- Calculus -
**MathMate**, Thursday, February 10, 2011 at 12:40am
I get -4.7943 and +4.7943 for x=-0.1 and x=0.1.

You may want to redo those calculations.

The conclusion for part C is correct.

- Calculus -
**Nicole**, Monday, September 3, 2012 at 5:16pm
part C is wrong you should give us the right answer and explain please.

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