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Grade: 12th pass
        
Get the maximum value of x for given this inverse trigonometric function.
2 months ago

Answers : (1)

Aditya Gupta
1690 Points
							
 
hello dear student. note that x is a natural number so it will have to be positive.
hence the argument x/pi inside tan^-1(x/pi) is positive, so that value of tan^-1(x/pi) will lie in between (0, 90 deg) or (0, pi/2 radians). now consider the graph of function y= f(x)= tan^-1(x). you will observe that it is strictly increasing (bcoz dy/dx= f’(x)= 1/(1+x^2) which is always greater than 0). also, we can write pi/3 as tan^-1(√3).
hence, tan^-1(x/pi) less than pi/3 implies tan^-1(x/pi) less than tan^-1(√3). which means that x/pi should be less than √3.
or x should be less than √3*pi
now approx value of √3*pi is 5.44139.........
since x is a natural number less than 5.44139........., its max value has to be equal to 5.
kindly approve :)
2 months ago
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