# What is #lim_(xrarr0) ( 1 + 3x )^(1/x) #?

It is

Hence, we must use D'Hospital Law to calculate the limit.

#lim_(x->0)ln(1+3x)/x=lim_(x->0) ((d/dxln(1+3x))/(dx/dx))= lim_(x->0) 3/(1+3x)=3#

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The limit of (1 + 3x)^(1/x) as x approaches 0 is e^3.

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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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