The smallest possible root of the equation tan x = x lies in which interval?? Q3 above
The smallest possible root of the equation tan x = x lies in which interval?? Q3 above
Sandipkumar , 6 Years ago
Grade 11
Trigonometry> The smallest possible root of the equatio...
2 AnswersArun
Last Activity: 6 Years ago
Note that tan x > x in (0, pi/2). It is clear from the graph that the point of intersection lies in the interval (pi/2, 3pi/2) which corresponds to the smallest positive root of tan x - x = 0.
Regards
Arun (askIITians forum expert)
Aditya Gupta
Last Activity: 6 Years ago
consider f(x)= tanx – x
now f ’(x)= sec^2x – 1= tan^2x>=0
now, f(0)=0 so f(x)>0 for all x in (0, π/2)
now, in (π/2. π), f(x) is always negative.
now, f(π)= – π and lim x----> 3π/2- (f(x))= plus infinty
since f(x) is continuous in (π, 3π/2), it has to pass through zero inside this interval
so the smallest positive root lies in (π, 3π/2). option (c)
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