How do you find the slope of a tangent line using secant lines?

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Wataru
Sep 20, 2014

The slope of a tangent line can be approximated by the slope of a secant line with one of the end point coincides with the point of tangency. So, if the slope of the secant line from a to a+h is

#{f(a+h)-f(a)}/{h}#,

then we can better approximate the slope of the tangent line by the slope of secant line by making #h# smaller and smaller. Hence, we can find the slope of the tangent line #m# at #x=a# by

#m=lim_{h to 0}{f(a+h)-f(a)}/{h}#

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