The value of tan^-1x at x=6 is
a) does not exist
b) a finite value
c)π/4
d) π/3
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The value of tan^-1x at x=6 is
a) does not exist
b) a finite value
c)π/4
d) π/3
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Answer:
The correct answer is option (b) .
Step-by-step explanation:
Since we know that principal branch of [tex]\tan^{-1}x[/tex] is [tex](-\frac{\pi}{2},\frac{\pi}{2})[/tex]
So the domain of [tex]\tan^{-1}x[/tex] is R and range is [tex](-\frac{\pi}{2},\frac{\pi}{2})[/tex]
Hence the value of [tex]\tan^{-1}x[/tex], when [tex]x=6[/tex] is a finite number between [tex]-\frac{\pi}{2}[/tex] and [tex]\frac{\pi}{2}[/tex]
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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