Question

The value of tan^-1x at x=6 is

a) does not exist
b) a finite value
c)π/4
d) π/3​

Answer 1

Answer:

The correct answer is option (b) .

Step-by-step explanation:

Since we know that principal branch of $\tan^{-1}x$ is $(-\frac{\pi}{2},\frac{\pi}{2})$

So the domain of $\tan^{-1}x$ is R and range is $(-\frac{\pi}{2},\frac{\pi}{2})$

Hence the value of $\tan^{-1}x$, when $x=6$ is a finite number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$

Answer 2

The value of tan⁻¹x at x=6 is a finite value

tan⁻¹x  has domain R

Hence tan⁻¹x  exist  for x = 6  

For Principal values  Range  = (-π/2 , π/2)

This function is one to one.

Hence for a unique value of x , tan⁻¹x has a unique value

Hence tan⁻¹(6) has  a finite value

tan (π/4) = 1

Hence tan⁻¹(1) = π/4

=> tan⁻¹(6) ≠  π/4

tan (π/3) = √3

Hence tan⁻¹(√3) = π/3

=> tan⁻¹(6) ≠  π/3

Hence from the given options tan⁻¹(6) has  a finite value is correct option.

option b) is correct

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