APPM 1345/1350
Final Exam Solutions
Spring 2013
1. (8 points) Match the following functions to their graphs below. No explanation is necessary.
(b) y = 2|x|
(a) y = ln(x + 1)
(c) y = tan1 x
(d) y = sinh(x).
=
1
1
2u1/2 + C =
8
4
1 4x2 + C
(b) First simpl
APPM 1345
Exam 2 Solutions
Spring 2013
4
v(t) dt = 32. Then
(d) From part (b) we know that
0
1. (22 points) The velocity function (in meters/second) for a particle moving
along a line is v(t) = 8 t3 . For the interval 0 t 4, evaluate the
following:
vave =
APPM 1345
Exam 1 Solutions
Intervals
x<6
Spring 2013
1. (25 points) Consider the function y = x 6 x.
(a) Find the domain of the function.
y
y
concave down on (, 6)
The function is concave down throughout the domain.
(f) There are no inection points .
(g)
APPM 1345
Exam 3 Solutions
Spring 2013
(b) Solution 1: Use logarithmic differentiation.
y=x
x
ln y = ln x x
ln y = x ln x
1. (12 points) Match the graphs shown to the following functions.
No explanation is necessary.
(a) y = ex
(d) y = 4x
(b) y = ex
(e) y