anonymous
  • anonymous
lim=2tan(x/3)/x as x goes to 0
Mathematics
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
You must use L'Hopital's rule. Do you know how?
anonymous
  • anonymous
NO
anonymous
  • anonymous
\[\lim_{x \rightarrow 0} \frac{2\tan(\frac{x}{3})}{x}\] you can use the squeeze theorem here and get : \[\frac{-\pi}{2} < \tan(\frac{x}{3}) < \frac{\pi}{2}\] \[\frac{\frac{-2\pi}{2}}{x} < \frac{2\tan(\frac{x}{3})}{x} <\frac{ \frac{2\pi}{2}}{x}\] \[\lim_{x \rightarrow 0} \frac{-\pi}{x} = \lim_{x \rightarrow 0}\frac{\pi}{x} = \lim_{x \rightarrow 0} \frac{2\tan(\frac{x}{3})}{x} = \infty\] ^_^ correct me if I'm wrong

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

nikvist
  • nikvist
\[\lim_{x\rightarrow 0}\frac{2\tan\frac{x}{3}}{x}= \lim_{x\rightarrow 0}\frac{\frac{2}{3}\cdot\tan\frac{x}{3}}{\frac{x}{3}}=\frac{2}{3}\cdot\lim_{y\rightarrow 0}\frac{\tan y}{y}= \frac{2}{3}\cdot\lim_{y\rightarrow 0}\frac{1}{\cos^2y}=\frac{2}{3}\]
anonymous
  • anonymous
hmm, if you used l'hopital's rule and got that, then there must've been a mistake in my calculations ? ^_^
anonymous
  • anonymous
;-)
anonymous
  • anonymous
hmm, but I'm sure of my steps though
anonymous
  • anonymous
You derive the numerator and the denominator independently until you end up with an answer other than 0/0 or infinity/infinity. The limit is 2/3.
anonymous
  • anonymous
but yomary is not aware of this way, so I tried the squeze theorem, but somehow it gives me a different answer ,hmm
nikvist
  • nikvist
\[-\frac{\pi}{2}<\tan\frac{x}{3}<\frac{\pi}{2}\] ???
anonymous
  • anonymous
well, tanx is , can't tan(x/3) be too?

Looking for something else?

Not the answer you are looking for? Search for more explanations.