1. An object is thrown from the top of a 126 foot tall building with an initial velocity
of 80 ft./sec in the horizontal (x ) direction with an initial velocity of 64 ft/sec. in the
vertical (y) direction.
(a) Sketch a graph of the path of the object.
(b) Find the parametric equations that describe the velocity at any time t.
(c) Find the parametric equations that describe the position at any time t.
(d) Find the maximum height that the object attains.
(e) Find the speed of the object at its maximum height.
(f) Find when the object passes the top of the building on its way down.
(g) Find the distance of the object from the building at the time found in (f).
(h) Find the displacement of the object at the time found in (e).
(i) Find the total distance traveled at time found in (e).
(j) Find the speed with which the object strikes the ground.
(k) Find the distance from the building of the object when it strikes the ground.
(l) Find the total distance that the object travels. Show both the integral and the
value.
(m) Find the displacement of the object when it is on the ground.
2. Determine if each of the following sequences converge or diverge. Explain your
answer (This means: If the sequence converges find the limit. If the sequence
diverges show the limit does not exist.)
(a) 53
54
(n 5n 10)
tan 4n 7n 1
+−π
++
(b) 3
nn10
ln 2
101n 3n 1
+−
++
(c) 2
3
(4n 71n 10)
cos 5
3n 1
+−π
+
3. Find:
(a) 1
0
ln xdx
∫
(b) x
1
xe dx
∞−
∫
4. Use integrations by parts to find ∫ ex cos x dx. Calculators should not be used.
