Since m ( h ) {\textstyle m(h)} is the slope of the secant line joining ( 0 , f ( 0 ) ) {\textstyle (0,f(0))} and ( h , f ( h ) ) {\textstyle (h,f(h))} , at the limit we have that lim h → 0 m ( h ) {\textstyle \lim \limits _{h\to 0}m(h)} is the slope of the tangent line of y = f ( x ) {\textstyle y=f(x)} at the point ( 0 , f ( 0 ) ) = ( 0 , 0 ) {\textstyle (0,f(0))=(0,0)} .
Answer: lim h → 0 m ( h ) {\textstyle \lim \limits _{h\to 0}m(h)} represents the slope of the tangent line at the origin. {\textstyle {\color {blue}{\mbox{slope of the tangent line at the origin.}}}}
