Yeah so I'm really rusty with the basic calc stuff. Pretty much forgot how to do this.
x -> infinity x sin (1/x)
So from the limit laws we know that lim x -> a f(x) g(x) = lim x->a f(x) lim x-> a g(x)
However thats assuming both function's limits exist.
If I let f(x) = x and g(x) = sin (1/x), the limit of f(x) is just infinity while g(x) is 0.
Using arbitrarily large numbers I can see that the answer is 1 but I don't know how to prove it or get there in a proper way.