1) finding the limit of a function and actually plugging in the number might result in different output. the output is different when the function is not continuous. when a function is not continuous the function might have an output which differs than the possible limit. plugging in the number C is a constant while plunging the limit as x reaches C is not the same as C. the limit follows the pattern of the equation it follows. while f(c) does not need to follow the pattern. when a function is continuous the limit of the equation are equal to f(c).

2) the similarities between the slope and directives is that the slope can be the derivatives. when slopes are used with lines, then the slope is equal to the derivative. while in equations such as parabolas the slope differs from the derivatives. the slope would be x^2 and the derivative would equal to 2.