How do you find the limit of #tanx# as #x->pi#?

Answer 1

#lim_(x->pi) tan(x)=0#

This limit can be evaluated by simply substituting in #pi# since #tan# is continuous and defined at #pi#:
#lim_(x->pi) tan(x)=tan(pi)#
In case we have forgotten the value of #tan(pi)#, we can use the following identity to figure it out: #tan(theta)=sin(theta)/cos(theta)#
This gives: #tan(pi)=sin(pi)/cos(pi)=0/(-1)=0#
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Answer 2

The limit of tan(x) as x approaches pi is undefined.

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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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