54.
55.
1.
2.
3.
4.
(A) The description of temperature change here is an example of Case II:
the rate of change is proportional to the amount or magnitude of the
quantity present (i.e., the temperature of the corpse) minus a fixed
constant (the temperature of the mortuary).
(C) Since (A) is the correct answer to Question 54, we solve the d.e. in
(A) given the initial condition T(0) = 32:
Using T(0) = 32, we get ln (22) = C, so
To find k, we use the given information that T(1) = 27:
Therefore T = 10 + 22e−0.258t.
10 Sequences and Series
(B) converges to −1.
(C) Note that .
(D) The sine function varies continuously between −1 and 1 inclusive.
(E) Note that is a sequence of the type sn = rn with |r| < 1; also
