A particle moving back and forth along a straight line has position function given byx(t)=sin((t2))

x(t)=sin((t2))witht

tin sec. Its instantaneous velocityv(t)

v(t)att=2

t=2is given by the limit of the difference quotient:

v(2)=lim

h0

x(2+h)x(2)

h

.

v(2)=limh0x(2+h)x(2)h.

(a) Estimate its instantaneous velocityv(2)

v(2)att=2

t=2sec using a table of values (up to two decimal places).

(b) Using part (a), can you guess what the value of the limitlim

z0

sin(z)

z

limz0sin(z)zis? Explain your reasoning.