Question

Find the limit :

Answer 1

\[\lim_{x \rightarrow \infty} x[ \sin( \frac{ a }{ x }) - \tan(\frac{ a }{ x })]\]

Answer 2

\[\lim_{x \rightarrow \infty} x[ \sin( \frac{ a }{ x }) - \tan(\frac{ a }{ x })]\\\lim_{t \rightarrow 0} \frac1t[ \sin( at) - \tan(at)]\]distribute and you should find some familiar limits

Answer 3

You assumed x = 1/t
sin(at)/t - tan(at)/t = a -a = 0 ?

Answer 4

seems that way

Answer 5

Thanks so much, May you help me with another one ?

Answer 6

sure :D

Answer 7

but you should post separately

Answer 8

I will and tag your name.