is there a way to find the right/left side limits of equtaions without using a graphing calculator, for example:
lim x-> 7/2 + int (2x-1)
Well you're going to have to try to explain what you can. "int" normally means integral, but could mean integer. Integral seems more likely since this is a calculus/pre-calculus topic and integer makes so sense. It might be the greatest integer function, which looks like stairs. Anyway, I'm not a fortune teller and you're gonna have to try to do what you can to explain.
Ok. Well assuming it's the greatest integer function (not the least integer function), this means that all decimals will round down to the previous integer (positive ones). So int(5.5)=5. This graph makes clear jumps, so limits can be seen easily. First consider the point f(7/2) - if it exists and what it is if so. Then since you are taking a right-sided limit look at points to the right of this. Remember that the limit is what value it is approaching, not necessarily what the value is at the point.