# Calculus

posted by Abi

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.

1. MathMate

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.

2. Abi

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 don't 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 don't know why.....

3. MathMate

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.

4. Nicole

part C is wrong you should give us the right answer and explain please.

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