MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 11.
Do the following questions from Chapter 7 of your text book, and show all your work:
(1) Questions 46 and 48, on page 334.
(2) Questions 18 and 20, on page 342.
(3)
Math 106 Calculus I for Bio & Soc. Sci. Fall 2012
Instructor: Nitu Kitchloo
Homework 9.
(1) Find the most general antiderivative of the following functions:
(a)
(b)
(c)
(2) Compute the following integrals:
(a)
(b)
(3) Solve the following initial value pro
Homework #10 Solutions
Sinan Ozdemir
November 21, 2012
1. #14 on page 321
if we are to compute the area between the curves y = 1 , xy = 1, and y = x in terms of y then it helps to rst visualize
2
our region.
d
We know the integral that we must compute is
HW 6 Solution
October 22, 2012
1. This problem depends on the formula
d 1
1
f (x) =
dx
f (f 1 (x)
Furthermore, because both f 1 and g 1 exist, we must have f, g are one-to-one and onto.
1
1
(a) We rst note that since f (1) = 2, so that f 1 (2) = 1. Hence,
Homework 2 Solutions
1. A certain strain of bacteria that reproduces asexually triples its size every 45 days.
If after 180 days there are 1620 bacteria, how many bacteria were there originally?
Solution: Let N0 be the number of bacteria there are initial
Homework 8 Solutions
by Hongtan Sun
(1)
Solution: If the length of the sides of the right angle is x and y respectively, the area is
given by
1
A = xy.
2
As the hypotenuse is 10 cm long, by Pythagorean Theorem, x2 + y 2 = 102 , hence y =
100 x2 . This mea
PILOT
Calculus I for Biological and Social Sciences
Fall 2013
Problem Set 3
1 3 + 2 4
a. ) lim
2 2 + 4
4
b. ) lim
1 + 2
1. Evaluate the limits
2. Let
1
( ) = 2 cos ,
a.) Use a graphing calculator to sketch the graph of y = f (x).
b.) Show that
holds for
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2013
PROFESSOR: JOSE MANUEL GOMEZ
Homework 5. Due date Friday October 18, 2013
Please show all your work.
(1) (10 Points) Compute the derivatives of the following functions.
(a) (2 Points)
2x3
a(x) = 3x4 .
2
(
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2013
PROFESSOR: JOSE MANUEL GOMEZ
Answers Suggested Problems Chapter 5
Section 5.1 Do the following problems from the book: Problems 9, 10, 11, 12, 19, 35, 38,
48,
Answers
Problem 19 c = 0 and f has a local m
PILOT Learning
Calculus I for Biology & Social Sciences
Fall 2013
Problem Set 1
1. The number of bacteria in a certain culture increases from 5,000 to 15,000 in 10 hours.
Assuming that the number of bacteria in this culture is modeled by exponential growt
PILOT
Calculus I for Biological and Social Sciences
Fall 2013
Problem Set 2
1. Find the limits
2 1
a. ) lim
0 1
b. ) lim sin
2
c. ) lim 3 + 4 1
1
d. ) lim ln(1 )
0
3
2. Use the limit laws to evaluate each limit.
2 2
a. ) lim 2
2 2
2
1
b. ) lim
1 1
PILOT
Calculus I for Biological and Social Sciences
Fall 2013
Problem Set 5
1. Find the equation of the tangent line to the curve of the following equations at the given point.
2
a. ) = 3 2 ,
(1,3)
c. ) = ,
b. ) = ,
(2,1)
2 ( ) + 1
3( )
( )
b. ) =
[()]2
Math 106 Calculus I for Bio & Soc. Sci. Fall 2012
Instructor: Nitu Kitchloo
Homework 11.
7.1.2
(46)
(48)
7.2
(18)
(20)
7.3
(18)
After solving this equation we get
, therefore we have
Now we solve the integral separately, we will have the result:
(24)
(1)(a)
lim
h0
f (h) f (0)
|h| |0|
= lim
h
h
h0
h 0
= lim
h
h0
= lim 1 = 1
h0
lim
h0+
f (h) f (0)
|h| |0|
= lim
h
h
h0+
h0
= lim+
h
h0
= lim+ 1 = 1
h0
(1)(b)
Because the limit from below and limit from the right are not equal, the limit
as h tends to zero
Homework 1 Solutions
1. The functions f and g are dened below
f (x) =
g (x) =
x2 1
1
x
Find explicit descriptions and the domains of the following functions.
(a) f g
Solution:
1
1
x2
As for the domain of f g , rst notice that the domain of the square root
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 9.
Please show all your work.
(1) Find the most general antiderivative of the following functions:
2
(a) f (x) = x3 + 3 .
x
(b) g (x) = x + 3 x + 4 x.
(c) h(x) = sec2 (2
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 8.
Please show all your work.
(1) What is the largest area for a right angle triangle whose hypotenuse is 10 cm long?
(2) Find the dimensions of a right circular cylinde
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 10.
Do the following questions from Section 6.3 pages 321 and 322 of your text book, and
show all your work:
(1) Question 14.
(2) Question 16
(3) Question 26
1
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 6.
Please show all your work.
(1) 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, g (2) = 2, g (1) = 3, g
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 4.
Please show all your work.
(1) Use the intermediate value theorem to show that there exists some x in the interval
[0, ] for which
2
2x
.
cos(x) =
(2) Show that the p
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 5.
Please show all your work.
(1) Consider the function f (x) = |x|.
(a) Compute
lim
h0
f (h) f (0)
f (h) f (0)
and lim+
.
h0
h
h
(b) Use the above to conclude that f (0
Homework 4 Solutions
(1)
x
Let f (x) = cos(x) 2 . f is a continuous function, f (0) = cos(0) 0 = 1 > 0,
and f ( 2 ) = cos( 2 ) 1 = 1 < 0. By the intermediate value theorem, there
exists some c in the interval 0, for which f (c) = 0. Therefore, there exist
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 1.
Please show all your work.
(1) The functions f and g are dened below
f (x) = x2 1,
1
g (x) = .
x
Find explicit descriptions and the domains of the following functions
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 7.
Please show all your work.
(1) Consider the function f (x) = 2x + 2. Use a suitable the linear approximation on
the function f (x) to estimate 4.2.
(2) Suppose that
x
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 2.
Please show all your work.
(1) A certain strain of bacteria that reproduces asexually triples its size every 45 days.
If after 180 days there are 1620 bacteria, how m
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2012
INSTRUCTOR: NITU KITCHLOO
Homework 3.
Please show all your work.
(1) Determine if the following limits exist. When they do nd their value
(a)
lim ex+2 .
x 2
(b)
lim+
x 3
(c)
x3 27
.
x3
ex + 1
.
x 0 3x + 1
MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2013
PROFESSOR: JOSE MANUEL GOMEZ
Homework 3. Due date Friday September 27, 2013
Please show all your work and explain your answers.
(1) (10 Points) Determine if the following limits exist. When they do nd the
Johns Hopkins University, Department of Mathematics
Calc I (Bio) - Spring 2013
Final Exam
Instructions: This exam has 7 pages (including a blank). No calculators, books, or notes are allowed.
Show all work for all problems. No credit will be given for ans