Exam I 151
(Show all work)
Seonghwa Park
October 7, 2013
2x + 1
1. Let f x = 3
x2 2
if x > 3
if x = 3
if 0 < < 3
(1) Find domain and range of the function f.
(2) Evaluate the limits limx3+ f(x), limx3 f(x) and limx3 f(x) if they exist.
(3) Is f(x) continu
Exam II 151
(Show all work)
Seonghwa Park
November 13, 2013
Find the derivatives of the following functions in Problems 1-6.
1. y = ecos
3 (2x)
2. y = sin1 1 x 2
3. y =
sin
( Simplify for 0 < x < 1 )
2
cos 1
4. y = ln secx + tanx ( Simplify )
5. y = arct
AMS 151
Assignment #4
(Total 79 points)
Section 2.4 (25 points)
1. (a) The statement f(200) = 1300 means that it costs $1300 to produce 200 gallons of the
chemical.
(b) The statement f(200) = 6 means that when the number of gallons produced is 200, costs
AMS 151
Assignment #2
Section 1.5 (29 points)
1. Sin(3/2) = 1 is negative.
Cos(3/2)= 0
Tan(3/2) is undefined.
9. Sin (1) is negative
Cos (1) is positive
Tan (1) is negative.
3
3
10. The period is 2/3, because when t varies from 0 to 2/3, the quantity 3t v
Solutions to Homework #3
2.1(20 points)
1. v
s s(b) s(a) 400 135 265
km / hr (1)
t
ba
52
3
6. s (t ) et 1 s (2) e 2 1 s (4) e 4 1
(e 4 1) (e 2 1) e 4 1 e 2 1 e 4 e 2
v
m / sec (2)
42
2
2
8. a. v
v
s(t h) s(t )
s 3t 2
h
3(1 h) 2 3
h
plug in for values o
Solutions to Homework #9b
4.8(25 points)
1. The particle moves on straight lines from 0,1 1,0 0, 1 1,0 0,1 (1)
2. The particle moves on straight lines from 0,0 2,0 2,1 0,1 0,0
(1)
4. The particle moves on straight lines from 1,1 1,1 1, 1 1, 1 1,1 (1)
x 3c
Aug 24, 2011
Mathematics Placement Advice
for Zihao Wu (108256231)
Placement Level:
5
Course options: MAT 131, MAT 141, or AMS 151
Your choices for mathematics course are explained below. AMS 151 and MAT 141 are
intended for especially well-motivated stud
Solution Key
Loretta Au
Quiz #1: Applied Calculus I (Fall 2011, Section 2)
Sept. 13, 2011
Instructions. This is a closed-book quiz worth 10 points, to be completed in 10 minutes. No
calculators are allowed; leave nal solutions as expressions, if necessary
Homework 8:(79 points)
4.1
2)(1) one critical point at x=2 one inflection point at x=4
3)(1) 2 critical points a local min and a point which is neither a local max nor local min
4)(3) to find the critical points, set f(x)=0: () = 3 2 18 + 24 = 0
To find t
EXAMS
EXAM PRACTICE QUESTIONS - PART 1
THIS REVIEW PAGE DOES NOT IMPLY THAT THE ACTUAL
MIDTERM QUESTIONS WILL BE OF THE SAME FORMAT.
1.
(a) n + (1+2+.+n) = n + n(n+1)/2
(b) O(n^2)
2.
(a) 10 * 16N/N = 160 min
(b) 10 * (16N)^2/N^2 = 2560 min
(c) 10 * (16Nlo
CSE 214 SUMMER 2017
Recitation #1 (TA Version)
1. [5 minutes] Write the order of complexity for the following programs using Big O notation if the programs execute the following number of operations for n inputs:
b) 4n + 5n2 + n4
a) 6n + 7
d) 2n + n1000
e
CSE 214 SUMMER 2017
Recitation #4 (TA Version)
1. [20 minutes] Write a recursive method to flatten the binary tree as follows:
The header of the method should be:
public static void flattenTheTree(TreeNode tree)
Solution:
public static TreeNode lastNode(T
CSE 214 SUMMER 2017
Recitation 2 (TA Version)
1. Given an array, a linked list, and a doubly linked list, determine which structure(s) would be better
for storing a collection in the following situations (and explain why)
a) Elements are usually accessed
EXAMS
PRACTICE QUESTIONS - MIDTERM 2
THIS REVIEW PAGE DOES NOT IMPLY THAT THE ACTUAL
MIDTERM QUESTIONS WILL BE OF THE SAME FORMAT.
1. Complete the following method that reverses the elements of an integer queue recursively. By reversing
the queue, we mean
CSE 214 SUMMER 2017
Recitation #5
TA Version
1. [10 minutes] Given the keys cfw_481, 433, 283, 199, 454, 679, 899, a fixed table
size of 10, and a hash function of H(k) = k mod 10, show the resulting:
(a) linear probing hash table
(b) quadratic probing ha
CSE214 Summer 2017
Recitation 6 (TA Version)
1. [23 minutes] Counting Sort:
So far we have seen that the best possible sorting algorithm performs in O(nlgn)
following sorting algorithm also known as Counting Sort:
time. Consider the
void counting_sort(int
CSE 214 SUMMER 2017
Recitation #3 (TA Version)
1. [20 minutes] Design a recursive method which prints first element of the list, then the last element of
the list, then second element of the list, then penultimate element of the list and so on e.g., for l
EqualsMethod:
As explained during the first recitation, one of the methods defined in the Object class is equals
method. Its signature is:
public boolean equals(Object o)
This method tests whether two objects are equal or not. The syntax for invoking it i
Solution Key
Loretta Au
Homework 14: Applied Calculus I (Fall 2011, Section 2)
Sept. 29, 2011
Selected homework problems. Here are detailed solutions to homework problems that students appeared to have the most trouble with on WebWork.
HW1: problem 9
HW
Solution Key
Pre-requisite Test: Applied Calculus I (Fall 2011, Section 2)
Loretta Au, instructor
Instructions. This is a closed-book exam to be completed in 40 minutes. No calculators are
3
allowed, so please leave your nal solutions as expressions, if n
AMS 151: Applied Calc
I
Lecture 17
Theorems about differentiable functions
Using the derivative
Viacheslav Zhygulin
Theorems about differentiable
functions
Theorems about differentiable
functions
Theorems about differentiable
functions
Theorems about diff
AMS 151: Applied Calc
I
Lecture 19
Using the derivative: optimization
Viacheslav Zhygulin
CHAPTER 4
Review:
Review:
Review:
Review:
Review:
Review:
Review:
Review:
Using first and second derivative:
Using first and second derivative:
Using first and secon
AMS 151: Applied Calc
I
Lecture 20
Rate of change
LHopitals rule
Parametric equations
Viacheslav Zhygulin
How do we measure a distance
traveled:
How do we measure a distance
traveled:
How do we measure a distance
traveled:
How do we measure a distance
tra
AMS 151: Applied Calc
I
Lecture 26
Final Practice Exam
Viacheslav Zhygulin
Final:
Structure the same as for midterm exam. 6 problems:
1. Find limit of the function. May involve LHopitals rule, squeeze theorem.
2. Prove statement. May involve any theorems