Finding the slope of a curve is different from finding the slope of a line. Explain why a limit is needed.?

I'm a beginner in Calculus 

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  • ?
    Lv 7
    1 month ago
    Favorite Answer

    You can find the slope of a line by calculating delta-y/delta-x using any two distinct points on the line.  On a curve, if you pick two points close together, the slope of the line between those two points will be close to the slope of the line tangent to the curve at either point, but the exact slope of the tangent line at a particular point can be found only by putting two points "infinitely close together" -- which is impossible.  The limit tells you what value is approached as the two points get closer and closer together.

  • 1 month ago

    You need 2 points on a line to find its slope. But a curve had a different slope at each point. So you must find its slope from 1 point. But that is not possible. So we use 2 points and make them closer and closer together. In the limit, as this distance goes to 0, gives us the slope of the curve at that point. This is called the derivative. 

  • Alan
    Lv 7
    1 month ago

    The slope of a line is a constant value. 

    It can be found using a limit also.  

    The slope of a curve can be continuously changing, so 

    a limit lets you find the rate of change at a particular point 

    or the instantaneous rate of change. 

    Slope = change in y/  (change in x)   

    In a line, this is always a constant value. 

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