1. the difference between the limit of x=c and plugging in x=c is that, taking the limit of something is when the point is being approached from the negative and positive ends, and there may be many different answers. But plugging in x=c you have one exact answer for the function.
2. the similarity of finding the derivative and the slope of a line is that you are really finding the slope of a line on both. the derivative is finding a slope of a curve but to do that you need to find the slope of the tangent line for the function. the difference is that for the derivative you are actually finding the slope of a curve.
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