Math 105: Review for Exam I - Solutions
1. Let f (x) = 3 + x + 5 .
(a) What is the natural domain of f ? [5, ), which means all reals greater than or equal to 5
(b) What is the range of f ? [3, ), which means all reals greater than or equal to 3
2. For th
Math 105 C
1. Find
Exam 02 ver01 page 1
11/08/2013
Name
dy
in each case below.
dx
1A) y = x + 3x + x3 + x + e +
x3 + 3x2
5x + 11
1B) y = tan(x3 + log2 (x)
1C) y = cos1 (x3 ) + (cos(x3 )1 + cos2 (x3 )
Hint Youll nd this much easier if you rewrite the rst a
Math 105 C
Exam 01 ver01 page 1
10/04/2013
Name
1. The following is the complete graph of some function s (x) (this is not the graph of s(x) which is not shown).
Answer the following questions about s(x), s (x) and s (x). Write any intervals in the form (
Math 105 C Exam ()2 verOl page 1 11/08/2013 Name
dy
1. Find in each case below.
1A)y=7r7+3z+r3+if"+e+:::3
3 z
77*! +11 2x+éx)~(5)(x +3x)
51/:(n w)rr"+(ln 3)3x+ 3x71 77x + o + X ( (5X HIP
1B) y = tan(a:3 +10g2(x))[umf: 741? X 1") of (m x)?
DI 2
Name:
Exam 2 Math 105D
Show all your work to receive full credit for a problem. There are a total of 72
points on this test. Good luck!
1. (4 pts. each) If p(1) = 3 and p (1) = 2, nd f (1) for the following:
(a) f (x) =
ln x
+ p(x5 )
p ( x)
(b) f (x) = ep
Name:
Exam 1 - Math 105D
Show all your work to receive full credit for a problem. There are a total of 72
points on this test.
1. (6 pts) Find the equation of the line tangent to the graph of f at (1, 1), where f is
given by f (x) = 2x3 2x2 + 1.
2. (6 pts
Math 105: Review for Exam I
1. Let f (x) = 3 + x + 5.
(a) What is the natural domain of f ?
(b) What is the range of f ?
2. For the graph of f shown, answer the following.
(a) Evaluate the following.
f(x)
i. f (2)
4
3
ii. f (3)
iii. lim f (x)
2
x3
iv. lim
Name:
Final Exam
Show all your work to receive full credit for a problem. There are a total of 100
points on this test. Good luck!
1. (4 pts. each) Two children riding their bikes start at the same time and travel in the
same direction along a straight ro
Namezwh
Math 105: Fa112013
Exam 1 (version (,0): October 4
Correct answers accompanied by incorrect or incomplete work will not receive full credit.
I. (6 points) A portion of the graph of 9(33) = x3 32: is shown
(a) Draw the line tangent to 9(3) at .1
Name:
Math 105: Fall 2013
Exam 1 (version ): October 4
Correct answers accompanied by incorrect or incomplete work will not receive full credit.
1. (6 points) A portion of the graph of g (x) = x3 3x is shown below.
(a) Draw the line tangent to g (x) at x
Name:
Math 105: Fall 2013
Exam 2: November 8
Correct answers accompanied by incorrect or incomplete work will not receive full credit.
There is a unit circle on the last page of the exam.
1. (14 points) Consider a function f that has the following graph.