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

1 Answer

Mar 1, 2017

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

Explanation:

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#

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