The smallest positive root of the equation, tan x - x = 0 lies in

Question

The smallest positive root of the equation, tan x - x = 0 lies in (A)  (0, (π/2))  (B)  ((π/2) , π )  (C)  (π , (3π/2))  (D)  ((3π/2) , 2π )

Tardigrade Admin · Accepted Answer

It is clear from the graph that the curves y = tan x and y = x intersect at P in (π,3 π / 2) . Thus the smallest +ve root of tan x - x = 0 lies in (π,3π / 2) .

Q. The smallest positive root of the equation, tan x - x = 0 lies in

$(0, \frac{π}{2})$

$(\frac{π}{2}, π)$

$(π, \frac{3 π}{2})$

$(\frac{3 π}{2}, 2 π)$

None of these

It is clear from the graph that the curves y = tan x and y = x intersect at P in $(π, 3 π /2)$ .
Thus the smallest +ve root of tan x - x = 0 lies in $(π, 3 π /2)$ .

Q. The smallest positive root of the equation, tan x - x = 0 lies in

(0,2π​)

(2π​,π)

(π,23π​)

(23π​,2π)