Evaluate each of the following limits. Show all reasoning.

[ugeous]

lim (2 tan^2 x)/x^2
x->0

I am just uncertain about how to do this question. Do I find a derivative or something else? Just need some guidance.

Thanx.

 

[HallsofIvy]

If it were me, I would rewrite tan x as sin x/cos x and try to break the expression into parts.

 

[ugeous]

Remind me please, do you rewrite tan as sin/cos before taking derivative or after? I think it is before, but not 100% sure. Thanks

 

[Dick]

Halls is guessing you know the limit x->0 of sin(x)/x. If so just substitute it. Otherwise, use l'Hopital.

 

[HallsofIvy]

Remind me please, do you rewrite tan as sin/cos before taking derivative or after? I think it is before, but not 100% sure. Thanks

Why in the world would you take any derivative?

 

[ugeous]

Ooooh... I have thought of a completely different thing here. I understand it now.

thanks guys!

 

[ugeous]

just wanted to confirm with you guys (finding this topic a little difficult)

by converting tan^2x i get

lim 2sin^2x
x->0 cos^2x(x^2)

limit x->0 of sin^2x/x^2 gives 1 correct? then I am simply left with 2/cos^2x which gives me final answer 2. Am I correct? Thanks for help/comments.

 

[Dick]

Yes, that's it.