1. the diffdrence between using the limit as x=c and plugging in x=c is that when you are findding the limit you are findding all the points that are approching c from the positive end and the negative end. plugging in x=c you arer able to find the exact answer. the limit from the negative end does not have to equal the limit from the positive side.
2.the similarty between find the slop and the derivitive is that when you find the slope you are finding the slope of the line . finding the derivitive is findint the slope of the tangent line. the difference is that for derivative you could be finding the slope of and live not just a straight line.
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