MATH 203
Quiz 35 (Sec 4.4) ANSWER
Find the limits.
1. [4pts] lim
5t
t!0
3t
t
Let f (t) and g(t) be f (t) = 5t 3t and g(t) = t, respectively. Then
f (t) and g(t) are both dened and dierentiable on R. Indeed, f 0 (t) =
f (0)
is an indeterminate
5t ln 5 3t l
MATH 203
Quiz 36 (Sec 4.5) ANSWER
Use the guidelines (A. Domain, B. Intercepts, C. Symmetry, D. Asymptotes,
E. Intervals of Increase and Decrease, F. Local Maximum and Minimum
Values, G. Concavity and In
ection Points) to graph each of the following
funct
MATH 203
Quiz 34 (Sec 4.2) ANSWER
1. Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [1; 4].
f (x) =
x
x+2
f is continuous on [1; 4]; and dierentiable on (1; 4). Thus, from the
Mean Value Theorem, there exists c 2
MATH 203
Quiz 38 (Sec 4.7) ANSWER
A cylindrical can without a top is made using A cm2 of material. (Note A
is a xed constant.) Find the dimension that will maximize the volume of
the can.
2 pi r
h
r
The gure above illustrates the general case. We wish to
MATH 203
Quiz 37 (Sec 4.7) ANSWER
A farmer wants to enclose a rectangular eld with 600 m of fencing and
then divide it in half with a fence parallel to one of the sides of the rectangle.
What is the largest possible total area of the eld? What are the dim