Question

Heat Transfer In the study of heat transfer, the equation $x+\tan x=0$occurs. Graph $Y_1=-x$and $Y_2=\tan x$for role="math" localid="1647098211924" $x\ge 0$. Conclude that there are an infinite number of points of intersection of these two graphs. Now find the first two positive solutions of $x+\tan x=0$rounded to two decimal places.

Short answer

The solution set is$\left\{2.03,4.91\right\}$.

Step-by-step solution

Step 1. Given Information 

In the study of heat transfer, the equation $x+\tan x=0$occurs. Graph role="math" localid="1647098348129" $Y_1=-x$and role="math" localid="1647098371685" $Y_2=\tan x$for role="math" localid="1647098396464" $x\ge 0$. Conclude that there are an infinite number of points of intersection of these two graphs. Now find the first two positive solutions of$x+\tan x=0$ rounded to two decimal places.

Step 2. Each solution of this equation is the x-coordinate of a point of intersection of the graphs of Y1=-x and Y2=tanx for x≥0.

The graph of the given equation is

Step 4. There are an infinite number of points of intersection; the x-coordinates are the solutions that we seek. 

Using INTERSECT, we find

$x=2.03x=4.91$

The first two positive solutions are $\left\{2.03,4.91\right\}$.