Limits of Infinity involving trigonometric values

[racuna]

I know that when you are trying to solve an infinity limit, the best thing you can do is factor and simplify, but in this case do you factor out a sinx on the top or x^2 :?:

lim x>infinity sin^2x/x^2

 

[tkhunny]

Who told you that?

Try this: 0 <= sin²(x) <= 1

Do not get caught up in believing there is one best way to solve a large variety of problem types. Keep your mind open. Organized, creative thinking is far more important than memorization. Of course, exams usually test for the latter. Hmpf!

 

[stapel]

I'd like to chime in here and emphatically second TKH's comments. The hardest thing for me when integrating is figuring out which method(s) might work, and which will only make life harder.

You definitely don't want to limit yourself here. Learn and absorb as many "patterns" and rules as you can. You'll be grateful on the test. :wink:

Eliz.

 

[racuna]

Huh?

why is it less than or equal to 0 and not -1? Isn't that the range of a sinx function or is this just talking about sin^2x?

 

[stapel]

If you square the part that's between -1 and 0, what do you get?

Eliz.