Calculus

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.

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  1. 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.

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  2. 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.....

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  3. 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.

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

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