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Please help meeeeeee I’m stressingggg out

Please help meeeeeee I’m stressingggg out-example-1
User Adrian Sohn
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1 Answer

21 votes
21 votes

Answer:

  • see attached for the table
  • limit is 3

Explanation:

You want a table of values of the function sin(3x)/x as x nears zero, and an estimate of the limit of the function value as x → 0.

Table of values

The function f(x) = sin(3x)/x is an even function. That is ...

f(-x) = sin(-3x)/(-x) = -sin(3x)/-x = sin(3x)/x = f(x)

When f(-x) = f(x), the function is even. It is a reflection of itself across the y-axis. This means all of the function values for negative x-values are the same as for the corresponding positive x-values. We only need to fill in half the table to know what the other half looks like.

See the attachment for values calculated by a spreadsheet and rounded to 8 decimal places.

Limit

The table shows the difference from 3 gets smaller as x gets closer to 0. If we add more rows to the spreadsheet table (2nd attachment), we see that the value gets even closer to 3 as x nears zero. At x = 10^-7, we run up against the accuracy limits of the spreadsheet.

The limit of the expression is 3 as x approaches 0.

Please help meeeeeee I’m stressingggg out-example-1
Please help meeeeeee I’m stressingggg out-example-2
User Nickbusted
by
3.1k points