Evaluate each of the following limits. Show all reasoning.

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression (2 tan² x)/x² as x approaches 0. The subject area pertains to calculus, specifically limits and trigonometric functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore different methods for evaluating the limit, including rewriting tan x in terms of sine and cosine, and considering the application of l'Hôpital's rule. Questions arise regarding the appropriate timing for rewriting functions in the limit process and the necessity of derivatives.

Discussion Status

The discussion is active, with participants providing various approaches and confirming each other's reasoning. Some guidance has been offered regarding the limit of sin(x)/x as x approaches 0, and there is a recognition of different interpretations of the problem. A participant expresses clarity after considering an alternative approach.

Contextual Notes

There is some uncertainty regarding the application of derivatives and the rewriting of trigonometric functions, indicating a need for clarification on these concepts. Participants are navigating through their understanding of limits and trigonometric identities.

ugeous
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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.
 
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If it were me, I would rewrite tan x as sin x/cos x and try to break the expression into parts.
 
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
 
Halls is guessing you know the limit x->0 of sin(x)/x. If so just substitute it. Otherwise, use l'Hopital.
 
ugeous said:
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?
 
Ooooh... I have thought of a completely different thing here. I understand it now.

thanks guys!
 
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.
 
Yes, that's it.
 

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