Question

lim [a^x sin(b/a^x)], when a>1 is = ?
x->infinity

Answer 1

\[\lim_{x \rightarrow \infty} \frac{ a^x*\sin(\frac{ b }{ a^x } )}{ }\]

Answer 2

u knw sinx/x when limit x ....>0 ????

Answer 3

\[\lim_{x \rightarrow \infty} \frac{ \sin \frac{ b }{ a^x } }{ \frac{ 1 }{ a^x} }\]

Answer 4

multiply and divide by b

Answer 5

\[\lim_{x \rightarrow \infty} \frac{ b*\sin(\frac{ b }{ a^x }) }{ b*\frac{ 1 }{ a^x }}\]

Answer 6

=b

Answer 7

Thank you very much

Answer 8

here 1/x is there so as x goex to infinity so it will 1/infinity=0 finally
and comes to sin0/0 so we can apply lim x...>0 sinx/x

Answer 9

Yes, I got it. Thanks once again.