MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 1. Due date Wednesday September 7, 2011
Please show all your work.
(1) (5 Points) The functions f and g are dened below
f ( x) = x2 1 ,
1
g ( x) = .
x
Find explicit
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 3.
(1) (10 Points) Determine if the following limits exist. When they do nd their value
(a)
lim ex+2 .
x2
(b)
lim
+
x3
x3 27
.
x3
(c)
ex + 1
.
x0 3x + 1
li
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 4.
Please show all your work.
(1) (5 Points) Use the intermediate value theorem to show that there exists some x in
the interval [0, ] for which
2
2x
cos(x
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 5.
Please show all your work.
(1) (5 Points) Consider the function f (x) = |x|.
(a) (3 Points) Compute
lim
h0
f (h) f (0)
f (h) f (0)
and lim+
.
h0
h
h
Sol
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 6.
Please show all your work.
(1) (5 Points) Suppose that f and g are dierentiable functions such that
f (1) = 2, f (2) = 1, f (1) = 2, f (2) = 1
g (1) = 2
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 7.
Please show all your work.
(1) (5 Points) Suppose that f and g are dierentiable functions such that
f (1) = 2, f (2) = 1, f (1) = 2, f (2) = 1
g (1) = 2
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 8.
Please show all your work.
(1) (5 Points) Consider the function f (x) = 2x + 2. Use a suitable the linear approximation on the function f (x) to estimat
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 9.
Please show all your work.
(1) (10 Points) What is the largest area for a right angle triangle whose hypotenuse is
10 cm long?
Solution: Lets denote the
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 10.
Please show all your work.
(1) (6 Points) Find the most general antiderivative of the following functions:
2
.
x3
(a) (2 Points) f (x) = x3 +
Solution:
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 2.
(1) (5 Points) A certain strain of bacteria that reproduces asexually triples its size every
45 days. If after 180 days there are 1620 bacteria, how man
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Solutions Homework 1.
Please show all your work.
(1) (5 Points) The functions f and g are dened below
f ( x) = x2 1 ,
1
g ( x) = .
x
Find explicit descriptions and the domain
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 10. Due date Friday December 2, 2011
Please show all your work.
(1) (6 Points) Find the most general antiderivative of the following functions:
2
(a) (2 Points) f (x
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 2. Due date Wednesday September 14, 2011
Please show all your work.
(1) (5 Points) A certain strain of bacteria that reproduces asexually triples its size every
45 d
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 3. Due date Wednesday September 21, 2011
Please show all your work.
(1) (10 Points) Determine if the following limits exist. When they do nd their value
(a)
lim ex+2
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 4. Due date Wednesday October 5, 2011
Please show all your work.
(1) (5 Points) Use the intermediate value theorem to show that there exists some x in
the interval [
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 5. Due date Wednesday October 12, 2011
Please show all your work.
(1) (5 Points) Consider the function f (x) = |x|.
(a) (3 Points) Compute
f (h) f (0)
f (h) f (0)
an
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 6. Due date Wednesday October 19, 2011
Please show all your work.
(1) (5 Points) Suppose that f and g are dierentiable functions such that
f (1) = 2, f (2) = 1, f (1
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 7. Due date Wednesday October 26, 2011
Please show all your work.
(1) (5 Points) Suppose that f and g are dierentiable functions such that
f (1) = 2, f (2) = 1, f (1
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 8. Due date Wednesday November 2, 2011
Please show all your work.
(1) (5 Points) Consider the function f (x) = 2x + 2. Use a suitable the linear approximation on the
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011
INSTRUCTOR: JOSE MANUEL GOMEZ
Homework 9. Due date Wednesday November 16, 2011
Please show all your work.
(1) (10 Points) What is the largest area for a right angle triangle whose hypotenuse is
10 cm long
CALC FINAL REVIEW
DEFINITIONS
- Limit (precise delta epsilon): Let f be a fcn defined on some open interval that contains
the number a, but not necessarily including a. The limit of f(x) as x approaches a is L and
lim xa f(x)= L if for every number > 0 th