For problems 13:
The average resting heart rate for an adult is
act to speed it up or slow it down. Suppose hormone X speeds up heart I
art rate. A simple model for the combined effect of the hormones on heart rate, R. is:
around 80 beats per minute, but
Midterm 2 Solutions - Math 17C - Spring 2016
PROBLEM 1 [20 points]:
Suppose you are studying the impact of deforestation on a region of the Amazon rainforest. At the
beginning of your study, satellite imaging finds that the density of plant biomass in you
Math 17C - Week 3 Homework Problem Solution
A quantity of central importance in the spread of infectious diseases is the basic reproduction number
R0 , which gives the average number of new infections that each infected individual produces when
introduced
MATH 17C - MATERIAL FOR MIDTERM 1 - April 20, 2016
Chapter 10: Multivariable Calculus.
10.1
evaluate z = f (x, y).
determine the domain and range of z = f (x, y).
interpret surface plots of z = f (x, y).
find and plot contours of z = f (x, y).
interp
Name:
Quiz 1 - Math 17C - Spring 2016
PROBLEM 1: The Body Mass Index (BMI) of a person is dened by the equation
m
BMI = f(m,h) 2 E2
where m is the persons mass (in kilograms) and h is the persons height (in meters). An optimal BMI
is roughly considered
Name:
Quiz 4 - Math 17C - Spring 2016
PROBLEM 1:
Evaluate the double integral by reversing the order of integration:
Z 3Z 9
3
x3 ey dydx
0
x2
10
8
6
D
4
2
-1
1
2
3
4
The domain of integration D is shown above. To reverse the order of integration, we descr
Name: aligni
Quiz 2 - Math 17C - Spring 2016
PROBLEM 1: Consider the dose response curve
$2
902 + (21%)
p=g($,w)= 2 forxandw>0
where a: is the dose of a toxin (in mg), w is the weight of a person poisoned by the toxin (in kg), and
p is the probability o
Quiz 3 Solutions - Math 17C - Spring 2016
PROBLEM 1: DNA polymerases are enzymes that assemble nucleotides to build DNA. Suppose
the rate of DNA production depends on the concentrations of enzyme (E) and nucleotide substrates
(S) according to the function
Name:
Quiz 6 Solutions - Math 17C - Spring 2016
PROBLEM 1:
Suppose a drug for migraines is administered to a patient in a single injection of 5 mg into the blood
stream. Let x(t) be the amount of the drug (in mg) in the blood and y(t) be the amount of dru
Name:
Quiz 5 - Math 17C - Spring 2016
PROBLEM 1:
The eigenvalues
1,
2
and corresponding eigenvectors v1 , v2 of the matrix
1
=
2, v1 =
1
1
and
2
= 4, v2 =
x
y
1
1
1 3
3 1
are
Consider the system of dierential equations
8
dx
>
>
= x + 3y
>
< dt
>
>
>
: dy
Solution to Midterm I of MAT17C
Professor Qinglan Xia
1. Consider the function
2
f (x, y) = e yx .
(a) Determine and sketch the domain of f .
Solution: The domain of f is
D = (x, y) : y x2 .
Sketch it yourself.
(b) Sketch the level curve f (x, y) = e.
Sol
Solution to Practice Midterm II of MAT17C
Instructions. No calculator is allowed.
1. Consider dierential equations of the form
d
3
1
= Ax (t) where A =
.
6 4
dt
(a) Find the general solution of the system.
Solution: Solving
det (A I) = det
3
1
= (3 ) (4 )
Solution to Practice Midterm I of MAT17C
1. Let
f (x, y) = ln 16 x2 y 2 ,
determine and sketch the domain of f . Also sketch the level curve
f (x, y) = ln 7.
Solution: The domain of f is a disk
D = (x, y) : x2 + y 2 < 16 .
The level curve f (x, y) = ln 7
Practice Midterm II of MAT17C
Instructions. No calculator is allowed.
1. Consider dierential equations of the form
dx
3
1
= Ax (t) where A =
.
6 4
dt
(a) Find the general solution of the system.
(b) Find the solution with the initial condition x (0) =
0
.
Practice Midterm I of MAT17C
Instructions. No calculator is allowed.
1. Let
f (x, y ) = ln 16 x2 y 2 ,
determine and sketch the domain of f . Also sketch the level curve
f (x, y ) = ln 7.
2. Assume that z = x2 y + xy 2 , x = t3 and y = t. Compute dz when