# 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.

Related Calculus and Beyond Homework Help News on Phys.org

#### HallsofIvy

Science Advisor
Homework Helper
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

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

#### HallsofIvy

Science Advisor
Homework Helper
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 im simply left with 2/cos^2x which gives me final answer 2. Am I correct? Thanks for help/comments.

Science Advisor
Homework Helper
Yes, that's it.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving