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Please explain the method of finding period of a function e.g tan3x ?

Answer 1

James Adkins

This is a practical method:

Period of tan x --> #pi# Period of tan (3x) --> #(pi/3)# Period of #tan (x/3)# --> #(3pi)#

Period of sin x --> #2pi# Period of sin (3x) --> #(2pi)/3# Period of #sin (x/3)# --> #3(2pi) = 6pi#

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Answer 2

Adam Aguirre

To find the period of a function such as ( \tan(3x) ), you need to determine the smallest positive value of ( p ) for which ( \tan(3(x+p)) = \tan(3x) ) holds true for all ( x ).

The period of the tangent function is ( \pi ), so for ( \tan(3x) ), the period is ( \frac{\pi}{3} ). This is because the coefficient of ( x ) inside the tangent function affects the period.

Therefore, the period of ( \tan(3x) ) is ( \frac{\pi}{3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.