Use a table of values to estimate the value of the limit.

lim (tan 3x/tan 5x)
x--> 0

I have no clue what to do. Could someone please explain how to go about this problem.

Make a table where the first column is x, the second column is tan(3x), the third is tan(5x), and the last is tan(3x)/tan(5x).

Set your calculator to radians, and calculate the values of tan(3x) and tan(5x) for x=0.1, 0.01, 0.001...

From the values suggested by the last column, conclude the value of the limit.

To estimate the value of the limit using a table of values, you can first create a table where you calculate the expression tan(3x)/tan(5x) for values of x that approach the limit, which is x = 0 in this case.

To start, choose a small increment for x, such as 0.1, and calculate the expression for values of x close to 0. Fill in the table with these values.

Let's create a table for x and the corresponding values for tan(3x)/tan(5x):

x | tan(3x)/tan(5x)
--------------------
-0.1 | -0.015
-0.01 | -0.0015
-0.001| -0.00015
0 | ?

As x approaches 0, calculate the expression for smaller and smaller values of x. However, taking the limit for this expression is not straightforward, and it is not possible to find the exact value using only this table.

In this case, it is helpful to use a graphing calculator or software that can plot the expression to visualize the behavior around x = 0. By graphing the expression, you can observe the trend and estimate the limit.

Please note that the use of a graphing calculator or software is not necessary for every question involving limits, but it can be helpful in cases like this where the limit is not immediately apparent.