First slide

Introduction to limits

Question

$if L = \lim_{x \to 1} {(\log_{3} 3 x)}^{\log_{x} 3}, thenthe value of [L], where [.] represents the greatest integer function , is$

Moderate

Solution

$\lim_{x \to 1} {(\log_{3} 3 x)}^{\log_{x} 3} = \lim_{x \to 1} {(\log_{3} 3 + \log_{3} x)}^{\frac{1}{\log_{x} 3}}$
$= \lim_{x \to 1} {(1 + \log_{3} x)}^{\frac{1}{\log_{x} 3}} (1^{\infty} form)$
$= e$

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