How do you find $lim sin(2x)/x$ as $x->0$ using l'Hospital's Rule?

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Answer 1 · 2017-03-01T12:52:17

$lim_(x->0) sin(2x)/x = 2$

The limit:

$lim_(x->0) sin(2x)/x$ is in the indeterminate form $0/0$ so we can solve it using l'Hospital's rule:

$lim_(x->0) sin(2x)/x = lim_(x->0) (d/dx sin(2x))/(d/dx x) = lim_(x->0) (2cos(2x))/1 = 2$

How do you find lim sin(2x)/xlim sin(2x)/x as x->0x->0 using l'Hospital's Rule?