Question
Sun November 11, 2012 By:
 

The smallest positive root of the equation tanx - x = 0 lies in (a) (0,pi/2) (b) (pi/2,pi) (c) (pi,3pi/2) (d) (3pi/2,2pi)

Expert Reply
Mon November 12, 2012
Draw the graph of y = x and y = tan x in the interval [0, 2?]
 
 
Note that tan x > x in (0, ?/2). It is clear from the graph that the point of intersection lies in the interval (?/2, 3?/2) which corresponds to the smallest positive root of tan x - x = 0.
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