calculus questions?

Question

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion, x(t) where t is in seconds and x in centimeters, is given below.
http://img218.imageshack.us/img218/4584/3335wr2.gif
x(t) = 10 sin(t)

(a) Find the velocity, v, and acceleration, a, at time t.

v(t) =

a(t) =

(b) Find the position, x, velocity, v, and acceleration, a, of the mass at time t = pi/ 3.

x ( pi)/3) =

v ( pi)/3) =

a ( pi)/3) =

In what direction is it moving at that time?
The particle is moving to the right, because of (velocity=0, velocity<0, velocity>0, acceleration=0, acceleration<0 or aceleration>0)

Answer 1

v(t) =10cos t cm/s
a(t) = -10sint cm/s^2
b) x= 5sqrt(3)
v= 5cm/s
a= -5 sqrt(3 ) cm/s^2
The particle is moving in the positive sense(right) because v>0
The velocity is decreasing as a<0

Answer 2

This lim is inderterminate (0/0) yet you have precluded using L'Hopital's Rule. So..... e^x = a million + x + x^2/2 + ........ As x is going to 0 then e^x is going to a million + x as a result your decrease will become lim (a million + h - a million)/3h = a million/3 lim a million = a million/3 with all the above limits as h has a tendency to 0. pass in peace....