Note: This is for a Calculus 1 course that has just started, so appropriately I can only use algebra/trig to solve these
I know sin(1/x) is always between 0 and 1, but sin(1/x) is getting close to 0 as x approaches infinity (sin of something close to 0 is close to 0), and so I'm getting infinity * 0 which doesn't really make any sense.
How can I show my work algebraically?
I have a similar problem though, but not sure if I need to create a new thread:
sinx/x as x approaches infinity
if I use substitution again, and use 1/u for x, I get lim as (1/u) approaches 0, sin(1/u)/(1/u) which is just 1, but that's incorrect... (since, intuitively I know that sinx will oscillate between 0 and 1, but the denominator will grow larger infinitely, therefore should theoretically approach 0 but that's just my thinking and no hard evidence)