No Taylor

Calculus Level 3

lim ⁡ x → 0 ( sin ⁡ x x ) 1 x = ? \displaystyle \lim_{x \to 0} \left (\frac{\sin x}{x}\right)^\frac{1}{x} = \, ?


The answer is 1.

Andrea Virgillito by Andrea Virgillito , 22, Italy

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2 solutions

Andrea Virgillito
Feb 12, 2017

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Christian Daang
Feb 24, 2017

it is just equal to:

( lim ⁡ x → 0 ( sin ⁡ x x ) ) ( 1 x ) = 1 ( 1 x ) = 1 \displaystyle \left( \lim_{x \rightarrow 0} \left( \cfrac{\sin x}{x} \right) \right)^{\left( \cfrac{1}{x} \right)} \\ = 1^{\left( \cfrac{1}{x} \right)} \\ = \boxed{1}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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