Lim 3x/tan3x x →0 How to solve it ? I think the answer will be 1 or -1 who can solve it ?

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Answer 1 · 2018-03-07T17:41:12

The limit is #1#.

#Lim_(x -> 0)(3x)/(tan3x)#

=#Lim_(x -> 0)(3x)/((sin3x)/(cos3x))#

=#Lim_(x -> 0)(3xcos3x)/(sin3x)#

=#Lim_(x -> 0)(3x)/(sin3x).cos3x#

=#Lim_(x -> 0)color(red)((3x)/(sin3x)).cos3x#

=#Lim_(x -> 0)cos3x#

=#Lim_(x -> 0)cos(3*0)#

#= Cos(0) = 1#

Remember that:

#Lim_(x -> 0)color(red)((3x)/(sin3x))=1#

and

#Lim_(x -> 0)color(red)((sin3x)/(3x))=1#