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.

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

To fill in the table of values for f(x), we can evaluate the function f(x)=sin(5x)/x for each given value of x.

(a)
To find f(x) for each value of x, we substitute x into the function f(x)=sin(5x)/x.

x= -0.1:
f(x) = sin(5*(-0.1))/(-0.1)
= sin(-0.5)/(-0.1)
≈ -0.4794

x= -0.01:
f(x) = sin(5*(-0.01))/(-0.01)
= sin(-0.05)/(-0.01)
≈ -0.4938

x= -0.001:
f(x) = sin(5*(-0.001))/(-0.001)
= sin(-0.005)/(-0.001)
≈ -0.4975

x= -0.0001:
f(x) = sin(5*(-0.0001))/(-0.0001)
= sin(-0.0005)/(-0.0001)
≈ -0.4988

x= 0.0001:
f(x) = sin(5*(0.0001))/(0.0001)
= sin(0.0005)/(0.0001)
≈ 0.4988

x= 0.001:
f(x) = sin(5*(0.001))/(0.001)
= sin(0.005)/(0.001)
≈ 0.4975

x= 0.01:
f(x) = sin(5*(0.01))/(0.01)
= sin(0.05)/(0.01)
≈ 0.4938

x= 0.1:
f(x) = sin(5*(0.1))/(0.1)
= sin(0.5)/(0.1)
≈ 0.4794

The filled table of values for f(x) is:

x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1
f(x)= -0.4794 -0.4938 -0.4975 -0.4988 0.4988 0.4975 0.4938 0.4794

(b)
Based on the table of values, as x approaches zero (x->0), we can observe that the values of f(x) are approaching 0. The limit of f(x) as x approaches zero is therefore:

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

(c)
To graph the function and find the interval near zero where the difference between the conjectured limit and the value of the function is less than 0.01, we can use a graphing tool or software.

By graphing the function f(x)=sin(5x)/x, we can observe that the graph approaches 0 as x approaches 0. To find the interval where the difference is less than 0.01, we need to find the x-values that correspond to a y-value in the range of (-0.01, 0.01).

The window that satisfies the conditions is:

-0.025 <= x <= 0.025
-0.01 <= y <= 0.01

Therefore, the window is:

-0.025 <= x <= 0.025
-0.01 <= y <= 0.01

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.....

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.

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.