Question

limℎ→0(1+ℎ)1ℎ=____________

Answer 1

Answer:

HEY MATE HERE'S YOUR ANSWER

Step-by-step explanation:

$The \: limit \: presents \: an \: undefined \: form \: \frac{0}{0} . In \: this \: case, \: you \: may \: use \: de \: l'hospital \: theorem, \: that \: states \\ \\ lim \frac{f(x)}{g(x)} =lim \frac{ f'(x)}{g'(x)} \\ \\ </p><p>The \: derivative \: of \: the \: numerator \: is</p><p> \frac{1}{ 2\sqrt{1 + h} } \\ While \: the \: derivative \: of \: the \: denominator \: is \: simply \: 1 \\ </p><p></p><p>So,</p><p></p><p>limx→0 \frac {f'(x)}{g'(x)}=limx→0 \frac{ 12√1+h1}{1}limx→0 \frac{1}{ 12√1+h} \\ and \: thus \: simply \frac{1}{2 \sqrt{1} } = \frac{1}{2} </p><p></p><p></p><p>$

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