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Prove that the least positive value of x...

Prove that the least positive value of `x ,` satisfying `tanx=x+1,` lies in the interval `(pi/4,pi/2)`

Text Solution

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Let `f(x)=tan x " and " g(x)=x+1,` which can be shown as follows.

From the figure, `tanx =x+1` has infinitely many solutions but the least positive value of x lies in `((pi)/(4),(pi)/(2)).`
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