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grace77

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What is the limit of sin2x/x as x approaches 0?Revelant equations

lim sin(x)/x = 1 x-->0

Attempt at a solution

so sin2x/x = 2sin(2x)/2x since sin(2x)/2x = 1 2sin(2x)/2x = 2*1

I know how to solve it this way however my teacher said you can solve it using double angle identity.

Sin2x= 2sinxcosx

That would be equal to lim2sinx/x * cosx/x

2sinx/x=2 but what would cos x/x when x approaches zero.. isn't that undefined? How do you figure that out then?