The difference is that when you are trying to find the limit as x approaches c, you are trying to find where the function is discontinuous coming from either the positive or negative or both sides. It can give you two different outputs. When you are plugging in c for a function, you get an exact point. The two cases are the same when the discontinuity is removable, you can get an exact point like when you plug in the constant.
Some similarities are that in the end, you are still looking for a slope. You use a formula in order to find both of the slopes. A difference would be that when you find the slope of a derivative, you are looking for the slope of the tangent line, and when you are looking for the slope of a line, you are just looking for the slope of a specific line.
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isnt finding the slope of a tangent line the same thing as finding the slope of a specific line?
ReplyDeletebtw, removable discontinuities do not make those two the same.