Question

÷id="TexFormula1" title="\lim_{x\to \ 0^{+} } (1+x)^{\frac{4}{x} }" alt="\lim_{x\to \ 0^{+} } (1+x)^{\frac{4}{x} }" align="absmiddle" class="latex-formula">

Answer 1

Answer:

e^4

Step-by-step explanation:

$\text{Let L=} \lim_{x \to 0+} (1+x)^{4/x}$

Take log both sides

$\log{L}= \lim_{x \to 0+} \frac{4\times log(1+x)}{x}\\\text{Apply L'Hopital}\\\log{L}=\lim_{x \to 0+} \frac{4\times 1}{1+x}\\\log{L}=4\\L=e^4$