What is the limit as x approaches 0 of #tan(x)/(3x)#?

Answer 1

The limit should give a 0/0 indeterminate form but using de l'Hospital Rule you should get 1/3 as result.

You can derive the numerator and denominator and do the limit of the new fraction obtained Deriv. Num = 1/ #cos^2(x)#

Deriv. Denom. = 3

Now you are left with: Lim[( 1/ #cos^2(x)#)/3] when x->0 you get 1/3
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Answer 2

The limit as x approaches 0 of tan(x)/(3x) is 1/3.

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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.

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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