anonymous
  • anonymous
Find the limit: x to infinity xsin(2/x)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Break it up in parts lim x and lim sin 2/x. For sin 2/x, look in your notes for what happens when a number say a is over in finity. Therefore it becomes sin of that quantity.
anonymous
  • anonymous
however i am not getting the answer by applying the limit the following way: |sin(2/x)|<= 1 so |xsin(2/x)|<=|x||sin2/x| triangle inequality now if i apply limit, lim |x|=infinity since it diverges, the smaller ones are bound to diverge. but in effect the answer is 2
anonymous
  • anonymous
How do you get 2, rsaad2?

Looking for something else?

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

More answers

anonymous
  • anonymous
can someone explain as to why? you use taylor polynomial, you get 2, but with comparison test you get infinity. confused ;S
anonymous
  • anonymous
Why are you going into higher mathematics? Why not Cal I limits?
anonymous
  • anonymous
as in?
anonymous
  • anonymous
like i said i am using simple limit, i am getting infinity.
anonymous
  • anonymous
Saw a similar example in my text book. Looking it up, I'll get back...
anonymous
  • anonymous
okay. here it is lim x (2/x) {sin(2/x)/ (2/x)} lim 2 lim {sin(2/x)/ (2/x)} 2*1 2
anonymous
  • anonymous
and the reason as to why sin(2/x)/(2/x) = 1 is because its similar to sin x/x when x-> 0 so lim sin x/x = 1.
anonymous
  • anonymous
Yeah, I was researching for my own learning. The proof is let u =sin 2x, then x = 2/u; limits changed to u goes to zero. It becomes limit as u goes to zero of (2 sin u)/u. Of course (sin u)/u is an identity equal to one. Therefore answer two. Good job rsaad2.

Looking for something else?

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