Page 91 - Calculus Demystified

Foundations of Calculus
CHAPTER 2
78 It follows that v 0 = 0, thus confirming our intuition that the initial velocity
is 0. Thus
2
p(t) =−16t + h 0 .
Now we also know that p(5) = 0; that is, at time t = 5 the ball is at height 0.
Thus
0 = p(5) =−16 · 5 + h 0 .
2

We may solve this equation for h 0 to determine that h 0 = 400.
We conclude that 2
p(t) =−16t + 400.
Furthermore, p(0) = 400, so the initial height of the ball is 400 feet.

You Try It: Suppose that a massive ball falls from a height of 600 feet. After how
lim TEAMFLY
many seconds will it strike the ground?

Exercises

1. Calculate, if possible, each of these limits. Give reasons for each step of
your solution.
x
lim x · e
(a) x→0
2
(b) x − 1
x→1 x − 1
(c) lim (x − 2) · cot(x − 2)
x→2
(d) lim x · ln x
x→0
2
(e) lim t − 7t + 12
t→3 t − 3
s − 3s − 4
2
lim
(f) s→4 s − 4
ln x
(g) lim
x→1 x − 1
2
(h) lim x − 9
x→−3 x + 3

Team-Fly
®