Question

For the function f(a)=asin(1/a), I have to find the limit as a approaches zero and as a approaches infinity. I know the answers, but I don't understand how to get there. Can someone explain it to me?

Answer 1

maybe make a change \(u=\frac{1}{a}\)

Answer 2

then
\[\lim_{a\to \infty}a\sin(\frac{1}{a})=\lim_{u \to 0}\frac{\sin(u)}{u}\]

Answer 3

Why does it equal the limit as u approaches zero? Why does it change from approaching infinity?

Answer 4

if you make the change \(u=\frac{1}{a}\) then as \(a\to\infty\) you would have \(u\to 0\)

Answer 5

clear or no?

Answer 6

Oh, that makes sense. That's why for when a approaches 0, when you replace it with u, it makes u approach infinity. Thanks so much!

Answer 7

yw