Let T = f t denote the temperature of a baked potato t minutes after it has been removed from a hot oven. The accompanying figure shows the temperature versus time curve for the potato, where r is the temperature of the room. (a) What is the physical significance of lim t → 0 + f t ? (b) What is the physical significance of lim t → + ∞ f t ?
Let T = f t denote the temperature of a baked potato t minutes after it has been removed from a hot oven. The accompanying figure shows the temperature versus time curve for the potato, where r is the temperature of the room. (a) What is the physical significance of lim t → 0 + f t ? (b) What is the physical significance of lim t → + ∞ f t ?
Let
T
=
f
t
denote the temperature of a baked potato
t
minutes after it has been removed from a hot oven. The accompanying figure shows the temperature versus time curve for the potato, where
r
is the temperature of the room.
(a) What is the physical significance of
lim
t
→
0
+
f
t
?
(b) What is the physical significance of
lim
t
→
+
∞
f
t
?
If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is
v = (mg/c)(1 − e^(−ct/m))
where g is the acceleration due to gravity and c is a positive constant.
A. Calculate lim(t→∞) v. What is the meaning of this limit?
B. For fixed t, use l’Hˆopital’s Rule to calculate lim(c→0+)v. What can you conclude about the velocity of a falling object in a vacuum?
*I missed a lecture on this topic, so more detail/explanation would be great!*
The percent of research articles in one prominent journal written by researches in the Unites States during 1983-2003 can be modeled by
A ( t ) = 12 + 28/1+.6(1.6)-t
where t is time in years since 1983. Numerically and/or graphically estimate lim x → ∞ A ( t ). (Do not include units or symbols.)
Chapter 1 Solutions
Calculus Early Transcendentals, Binder Ready Version
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