January 24, 2017

Homework Help: Calculus

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
( 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?

Note: You can earn partial credit on this problem.

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