1. The problem statement, all variables and given/known data 1. sin(1/x) as x->infinity 2. tan(7x)/sin(5x) as x->0 3. General question--when finding the derivative (through implicit diff.), and I have something like y=(5x^2)y, what parts am I supposed to use the chain rule, and when am I supposed to use the product rule? 3. The attempt at a solution 1. I literally have no idea how to do this. Possibly multiplying, but sin/sinx doesn't seem to get me anywhere. 2. sin7x/cos7x times 1/sin5x. Not quite sure what to do afterwards. 3. Is this correct? -- 10x^2(y) times y' ?