To estimate the limit of the function (sin(5θ)/θ) as θ approaches 0, we can create a graph to analyze the behavior of the function near θ = 0.
Let's plot the function y = (sin(5θ)/θ) on a graph.
First, we'll create a table of values for θ and compute the corresponding values of y:
θ | y = (sin(5θ)/θ)
--------|---------------
0.1 | 0.49736
0.01 | 0.499984
0.001 | 0.4999998
0.0001 | 0.5
0.00001 | 0.5
Now, let's plot these values on a graph:
|
y | #
| #
| #
| #
| #
| #
| #
| #
|-----------------
0 θ
As we can see, as θ approaches 0, the values of y seem to approach a constant value of 0.5.
Therefore, we can estimate that the limit of (sin(5θ)/θ) as θ approaches 0 is 0.5.