Limit as X goes to Infinity of sine 7X over 10X. We're going to use the sandwich or squeeze theorem to show that. We know to show that sine of 7X is going to be in between -1 and one. So if sine of X is in between -1 and one, if I can show that -1 or the left side and the right side are going to go to the same limit, then I know that the thing in the middle has to also go to the same limit. So the first thing we're going to do is we're going to take this inequality and divide every piece by 10X. We know that X is going to be positive because we're looking at what happens when X goes out to Infinity. So we have -1 / 10 X less than or equal to sine 7X divided by 10X less than or equal to 1 / 10 X. So now as the limit as X goes to Infinity of -1 / 10 X so -1 over something really, really, really big is going to be something really, really small, or it's going to go to 0. The limit as X goes to Infinity of 1 / 10 X one over something really, really big is going to be something really, really small. So if this piece goes to 0 and this piece goes to 0, by the sandwich or squeeze theorem we know that the piece in between has also got to go to 0.