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What are the asymptotes for #f(x) = tan(2x)#?

Answer 1

Benjamin Achtenberg

Note that #tan(2x)=sin(2x)/cos(2x)#.

This expression will form asymptotes when #cos(2x)=0#.

This expression is zero when #2x=+-(n+1/2)pi, n=0,1,2...#.

Therefore the asymptotes occur at #x=+-1/2(n+1/2)pi, n=0,1,2...#

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Answer 2

Elijah Allen

The asymptotes for the function (f(x) = \tan(2x)) occur when the tangent function approaches undefined values. Tangent is undefined at odd multiples of (\frac{\pi}{2}). Therefore, the asymptotes for (f(x) = \tan(2x)) are at (x = \frac{\pi}{4} + \frac{\pi}{2}k), where (k) is an integer.

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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.