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Chapter 5: Problem 53

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$x \tan x-1=0$$

Short Answer

Expert verified
Using a graphing utility, the approximate values within the range [0, 2蟺] where \(x\tan x = 1\) (or \(x\tan x - 1 = 0\) ) intersects the x-axis yield the solutions to this equation. The exact values will depend on the utility used, but should be approximated to the nearest thousandths (three decimal places) place.

Step by step solution

01

Understand the Equation

We are given the equation \(x \tan x-1=0\). This is a trigonometric function which utilizes the tangent function. This function can be transformed to \(x \tan x = 1\).
02

Graphing the Equation

The next step is to plot the function on a graphing utility. This can be done using software or an online tool. Input the equation \(x \tan x = 1\) and adjust the function's viewing range to be from \(0\) to \(2\pi\) on the x-axis.
03

Identifying the Solutions

Since the graphing utility enables us to view the function graphically, we can approximate the x values where the function intersects the x-axis since that's where the results of our function equal \(0\). Identify these points on the graph and use the trace function on the graphing utility to find rough estimates of these solutions, rounded to three decimal places.

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