Tangent problem. What is it?

peps
I'm starting my first lesson in Calc I this week and I have a question regarding limits and the tangent line.

I understand how to calculate the limit and determine the slope as Q approaches P. I also understand in connecting the two points with the secant line but I don't seem to understand the purpose of the tangent line.

Given point P, I can determine the slope and the limit by choosing other points along the curve. I choose a point Q and connect it to P with a secant line but what is the purpose of the tangent line? Is the point that the tangent and the graph crosses supposed to indicate the limit?

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