Ben has programmed a flying machine. Its horizontal speed
at time t (in minutes) is h(t) = 4t - 2 and its vertical speed at t (in
minutes) is v(t) = 6t^2 + 7t - 5. Ben is interested (for some strange rea-
son) in the quotient of vertical speed and horizontal speed. Determine
the limit of the quotient of vertical speed and horizontal speed as the
time approaches 30 seconds.
at time t (in minutes) is h(t) = 4t - 2 and its vertical speed at t (in
minutes) is v(t) = 6t^2 + 7t - 5. Ben is interested (for some strange rea-
son) in the quotient of vertical speed and horizontal speed. Determine
the limit of the quotient of vertical speed and horizontal speed as the
time approaches 30 seconds.
-
v(t) / h(t)
= (6t² + 7t - 5) / (4t - 2)
= (3t + 5)(2t - 1) / 2(2t - 1)
= (3t + 5)/2
As t approaches 30 the quotient approaches (3 x 30 + 5)/2 = 47.4
(but I'm not convinced that a flying machine that starts by flying backwards and DOWNWARDS is likely to catch on)
= (6t² + 7t - 5) / (4t - 2)
= (3t + 5)(2t - 1) / 2(2t - 1)
= (3t + 5)/2
As t approaches 30 the quotient approaches (3 x 30 + 5)/2 = 47.4
(but I'm not convinced that a flying machine that starts by flying backwards and DOWNWARDS is likely to catch on)