00:03
Alright, so the question is, by the limit is x equal to 0, upside 3x over tangent of x, fx, x, and we are not allowed to use an error hospital rule here.
00:28
And we only can use the fact that the limit is f x go to zero, upside f x over x is 1.
00:36
So we're going to make use of that identity.
00:39
So now note that using the definition of tangents of x, we can arrive to expression as follow.
00:49
Plus x is psi vx over side of x over cosy of x plus x.
01:01
And it is just cosy of x time si of vx over side of x plus x.
01:10
So to use the identity that syracx over x to make syab x over x appear we're going to divide both numerator and denominator of this by 3x.
01:29
It's just cosine x times side of x over 3x over side of x over 3x plus cosine of x over 3.
01:48
So now we're going to collect things...