# Solve the following (limit; L'Hospital's Rule)?

##
#\lim_(x\rightarrow0^+)(\tan(2x))^x#

**What I've tried**

#y=(\tan(2x))^x#

#\rArr\ln(y)=\lim_(x\rightarrow0^+)\ln((\tan(2x))^x)...#

*got stuck afterwards.*

#\lim_(x\rightarrow0^+)(\tan(2x))^x#

**What I've tried**

*got stuck afterwards.*

Of course, please provide the specific limit you would like to solve using L'Hôpital's Rule.

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then

now using the binomial expansion

Of course

Finally

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1

Let y = (tan 2x)^x, then

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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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