Where are the vertical asymptotes of #f(x) = tan x#?

Answer 1

The asymptotes are at #x=pi/2+kpi, x in ZZ#

The vertical asymptotes of a function are usually located in points, where the function is undefined. In this case since #tanx=sinx/cosx#, the asymptotes are located where #cosx=0# (denominator of a fraction cannot be zero) which leads to the answer: #x=pi/2+kpi, x in ZZ#
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Answer 2

The vertical asymptotes of the function ( f(x) = \tan(x) ) occur at odd multiples of ( \frac{\pi}{2} ). So, the vertical asymptotes are at ( x = \frac{\pi}{2} + n\pi ) and ( x = -\frac{\pi}{2} + n\pi ), where ( n ) 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.

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.

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.

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.

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