Consider the position function s(t) = -16t^2 + 100t in feet.
(a) Complete the following table with average velocities of the object between (1, s(1)) and (t, s(t)) for t = 2, 1.5, 1.11, 1.01, and 1.001. You may use a calculator. Round the final answer to three decimal places as needed.
Time interval [1, 2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001]
Vavg
(b) Make a conjecture about the instantaneous velocity at t = 1s.
Consider the function f(x) = 5 cos(x) and (x, f(x)) for x = π, π + 0.1, 2
(a) Find the slopes of the secant lines through π, π + 0.1, π + 0.01, π + 0.001, π + 0.0001. Round all intermediate values to four decimal places as needed. Write an integer or a decimal.
Interval
[π, π + 0.1] [π + 0.01] [π + 0.001] [π + 0.0001]
Slope of SL
(b) Make a conjecture about the slope mtan of the tangent line at x = 2.
