Limit of a Function

The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as unpredictably moving left, right, up, and down. For a typical knuckleball speed of 60 mph, the left/right position of the ball (in feet) as it crosses the plate is given by 1.7 5 f ( w ) = sin(2.72@) (derived from experimental data in Watts and Bahill's book Keeping Your Eye on the Ball), where w is the rotational speed of the ball in radians per second and where f (w) = 0 corresponds to the middle of home plate. Folk wisdom among baseball pitchers has it that the less spin on the ball, the better the pitch. To investigate this theory, we consider the lim, f(w). (1) Evaluate the lim f(@) using the graphical and tabular approaches. Use the first w-ot quadrant of the Cartesian plane in sketching the graph. (2) A knuckleball thrown with a different grip than that of the problem above has left/right position as it crosses the plate given by 0.625 f (w) = () 2 [1 - sin (2.72w + 7) Again, use graphical and tabular evidence to make a conjecture about the lim, f(w). w-0+