Question

1. give a geometrical interpretation of lim (text partially obscured)
2. use the graph to answer each question.

(graph of y = f(x) with points a, b, c, d, e)

a. between which two consecutive points is the average rate of change in the function the greatest?
b. is the average rate of change in the function between a and b greater than or less than the instantaneous rate of change at b?
c. sketch a tangent to the graph somewhere between points d and e such that the slope of the tangent is the same as the average rate of change in the function between b and c.

1. what is wrong with the statement “the speed of the cheetah was 65 km/h north”?
2. is there anything wrong with the statement “a school bus had a velocity of 60 km/h for the morning run, which is why it was late arriving”?

Explanation:

Sub - question 5

Speed is a scalar quantity, which only has magnitude. Velocity is a vector quantity that has both magnitude and direction. The statement uses "speed" with a direction ("north"), which is incorrect because speed does not include direction. It should use "velocity" if direction is to be specified.

Velocity is a vector quantity that includes both speed (magnitude) and direction. Saying a school bus had a velocity of 60 km/h without specifying direction is incomplete for velocity. Also, if we consider the context of being late, just stating a single velocity value doesn't explain why it was late (e.g., maybe it had variable speed or direction issues, but the main error is the incomplete definition of velocity here as it lacks direction, and also the causal link between a single velocity value and being late is not clear as velocity is about motion state, not necessarily directly about lateness without more context, but the primary physics - related error is the incomplete velocity definition).

Answer:

Speed is a scalar (magnitude only), but "north" is a direction. The statement incorrectly attributes direction to speed; it should use "velocity" (a vector with magnitude and direction) instead of "speed" when including direction.

Sub - question 6