Finding Instantaneous Velocity (3.1.2)

Question 1

• The average rate of change is equal to the slope of the secant line between the two points being considered. The instantaneous rate of change is equal to the slope of the tangent line at the point being considered.

Answer 1

• The average rate of change is equal to the slope of the secant line between the two points being considered. The instantaneous rate of change is equal to the slope of the tangent line at the point being considered.

Question 2

• By examining the average rate of change along an interval of length Δt, you can set the length to be as large or small as you like.

Answer 2

• By examining the average rate of change along an interval of length Δt, you can set the length to be as large or small as you like.

Question 3

• To find the instantaneous rate, take the limit of the average rate on the interval [t, Δt] as Δt approaches zero.

Answer 3

• To find the instantaneous rate, take the limit of the average rate on the interval [t, Δt] as Δt approaches zero.

Question 4

Instantaneous rates of change are found by:

Answer 4

Taking the limit of the average rate of change as Δt goes to zero.

Explanation:

The instantaneous rate of change is calculated by
taking the limit of the average rate of change as Δt
goes to zero.