APCR Deriv of Tan Line Problem

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If f is defined on (a,b) containing c then the lim as deltax approaches 0 =f(x+deltax)-f(c) over deltax=m then the line passing through (c, f(c)) w/slope m is the tan line to graph
If f is cont at c and f(c+deltax)-f(c) over deltax=p/m infinity then the vertical line x=c is a vertical tan line
f'(x)=lim as deltax approaches 0 f(x+deltax)-f(x)over deltax
deltay over delta x is the slope of a sec line but the lim as x approaches 0 delta y over delta x is the slope of a tan line
f'(c) = lim as x approaches c f(x) -f(c) over x-c
implies continuity but not vice versa

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