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endeavor
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Homework Statement
Compute the limit [tex]\lim_{x \rightarrow 0} (1 + 3x)^{3/x}[/tex].
Homework Equations
The Attempt at a Solution
[tex]\lim_{x \rightarrow 0} (1 + 3x)^{3/x} = \lim_{x \rightarrow 0} e^{\frac{3}{x} \ln (1 + 3x)}[/tex]
[tex]\lim_{x \rightarrow 0} \frac{3}{x} \ln (1 + 3x) = 3 \lim_{x \rightarrow 0} \frac{ln (1 + 3x)}{x}[/tex]
[tex]= 3 \lim_{x \rightarrow 0} \frac{\frac{3}{1 + 3x}}{1}[/tex]
[tex]= 3 \lim_{x \rightarrow 0} \frac{3}{1 + 3x}[/tex]
[tex]=9[/tex]
[tex]\lim_{x \rightarrow 0} (1 + 3x)^{3/x} = e^9[/tex]
I just need to know if this is right.
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