Sarah Herrmann
Assignment 13.5 COMPARISON TESTS due 03/15/2013 at 09:00am PDT
1. (1 pt) Determine whether following the series converges
or diverges.
MATH 009C 001 13W
5. (1 pt) Determine whether the
Sarah Herrmann
Assignment 12.4 PARAMETRIC EQUATIONS due 03/18/2013 at 09:00am PDT
MATH 009C 001 13W
1. (1 pt) Below you are given four parametric equations and
their plots. Match each plot to the corr
Suraj Patel
Assignment 12.4 PARAMETRIC EQUATIONS due 07/02/2015 at 08:00am PDT
A.
B.
C.
D.
E.
F.
1. (1 pt) Below you are given four parametric equations and
their plots. Match each plot to the correct
Sarah Herrmann
Assignment 13.12 ADDITIONAL EXERCISES due 02/11/2013 at 08:00am PST
MATH 009C 001 13W
n.5 + 3
2
n=1 n + 5
r=
converges or diverges (c or d)?
C.
1. (1 pt) Match each sequence below to st
Ting-Ju Liu
MATH 009C 020 17F
Assignment 8.7 8.8 TAYLOR POLYNOMIALS AND SERIES due 11/30/2017 at 11:59pm PST
5. (1 pt) The Taylor series for f (x) = sin(x) at a =
1. (1 pt)
n
n=0 cn (x 2 ) .
The func
8.1 Sequences
Chenxu Wen
1
Definition and basic examples
In real life, a sequence of evens means that the events occur in order, i.e. one after
another. In mathematics, we adopt the word sequence to r
Math 9C Final Practice 2
Instructions: This exam has a total of 100 points. You have 180 minutes.
You must show all your work to receive full credit. You may use any result done in class.
You are not
Math 9C Final Practice 3
Instructions: This exam has a total of 100 points. You have 180 minutes.
You must show all your work to receive full credit. You may use any result done in class.
You are not
Math 9C Final Practice 1
Instructions: This exam has a total of 100 points. You have 180 minutes.
You must show all your work to receive full credit. You may use any result done in class.
You are not
Midterm Exam
University of California, Riverside
Department of Mathematics
MATH 9C020 NAME:
Spring2017 (print)
In signing my name below I pledge that I have neither given nor received help on this exa
Taylor series
Mike Hartglass
February 24, 2017
Last time
I
I
Suppose f is smooth at a.
The Taylor polynomial of order n, centered at a is
f 00 (a)
(x a)2 +
2!
f (k) (a)
f (n) (a)
+
(x a)k + +
(x a)n
Limit comparison and ratio tests
Mike Hartglass
February 1, 2017
Limit comparison test
I
The limit comparison test: Suppose an and bn are positive
an
terms. and lim
n bn
I
I
exists and
is not 0 or
Th
Comparison and limit comparison tests
Mike Hartglass
January 30, 2017
The comparison test
I
Theorem: The comparison test: Suppose that an and bn are
nonnegative for all n.
I
I
P
P
If n=1 bn converges
Jannatin Nisha
Assignment 8.2 Infinite Series Part 2 due 10/26/2017 at 11:59pm PDT
Converges (y/n):
Value if convergent (blank otherwise):
1. (1 pt) Determine whether the series is convergent or diver
Jannatin Nisha
Assignment 8.2 Infinite Series Part 1 due 10/19/2017 at 11:59pm PDT
MATH 009C 020 17F
Converges (y/n):
Value if convergent (blank otherwise):
1. (1 pt) Find the sum
Answer(s) submitted:
Ting-Ju Liu
Assignment 8.6 POWER SERIES due 11/30/2017 at 11:59pm PST
5. (1 pt) Find all the values of x such that the given series
would converge.
(2x)n
n5
n=1
The series is convergent
, left end in
Ting-Ju Liu
Assignment 8.2 Infinite Series Part 1 due 10/19/2017 at 11:59pm PDT
Determine whether the series converges, and if it converges,
determine its value.
1. (1 pt) Find the sum
8 +
MATH 009C 0
Ting-Ju Liu
Assignment 8.2 Infinite Series Part 2 due 10/26/2017 at 11:59pm PDT
Converges (y/n):
Value if convergent (blank otherwise):
1. (1 pt) Determine whether the series is convergent or divergen
Ting-Ju Liu
Assignment Alternating Series due 11/09/2017 at 10:59pm PST
MATH 009C 020 17F
C
1. (1 pt) Determine whether the following series converges
or diverges.
n
(1)n 5 + ln n
n=1
5. (1 pt) Dete
Ting-Ju Liu
Assignment 8.4 RATIO AND ROOT TESTS due 11/02/2017 at 11:59pm PDT
MATH 009C 020 17F
5n
1. (1 pt) Use the ratio test to determine whether
2
n=8 (8n)
converges or diverges.
(a) Find the rat
Ting-Ju Liu
Assignment 8.3 Integral AND Comparison Test Part 2 due 11/02/2017 at 11:59pm PDT
5. (1 pt) Determine whether the following series converges
or diverges:
1. (1 pt) Determine whether followi
MATH 009C
PRACTICE FINAL
August 12, 2017
Score:
Name:
/ 100
Student ID:
DO NOT OPEN THE EXAM UNTIL YOU ARE TOLD TO DO SO
1
2
3
4
5
6
7
8
9
Total
200
25
25
25
25
25
25
25
25
25
210
X
Score
Pts. Possibl
MATH 009C - Summer 2017 - Syllabus
First Year Calculus III
Instructor: Josh Buli
E-mail: [email protected]
TA: Adam Yassine
Email: [email protected]
Website: www.math.ucr.edu/buli
Class Time: Section D0
Jannatin Nisha
Assignment 0.1 INTRODUCTION TO WEBWORK due 10/06/2017 at 11:58pm PDT
or even sinx. If you remember your trig identities, sin(x) = cos(x+pi/2) and WeBWorK will accept this or any other f
Power series
Mike Hartglass
February 13, 2016
Radius and interval of convergence
I
Theorem: For the power series
X
an (x a)n , exactly one of
n=0
the following is true:
1. The series converges at x =
Power series
Mike Hartglass
February 13, 2016
Integration and differentiation of power series
I
Theorem: Let f (x) =
I
X
nan (x a)
n=1
I
n=0 an (x
a)n
f is differentiable at every point inside its ra
Intro to power series/review
Mike Hartglass
February 8, 2017
Example
I
Example/Motivation: We have seen the following formula
X
n=0
rn =
1
1r
provided |r| < 1.
I
To but it another way, we can think of
Math 9C Final Practice 3
Instructions: This exam has a total of 100 points. You have 180 minutes.
You must show all your work to receive full credit. You may use any result done in class.
You are not
Math 9C Final Practice 2
Instructions: This exam has a total of 100 points. You have 180 minutes.
You must show all your work to receive full credit. You may use any result done in class.
You are not
Math 9C Midterm Practice 2
Instructions: This exam has a total of 60 points. You have 50 minutes.
You must show all your work to receive full credit. You may use any result done in class.
The points a
Math 9C: Calculus
Winter 2018
Midterm
02/09/2018
Time Limit: 50 Minutes
Name (Print):
Discussion TA:
Discussion time:
This exam contains 7 pages (including this cover page) and 4 problems. Check to se
9.3
Calculus and Parametric Equations
Aim:
Slope of the parametric equations
Arc length of curves
9.3.1
Derivatives: Tangent and Normal Lines
Theorem 1. Let x = x(t), y = y(t) be parametric equation
8.6
Power Series
8.6.1
Power Series
Definition 1. Let cfw_an be a sequence and let x be a variable, c a real number.
The power series in x centred at c is the series of the form
an (x c)n = a0 + a1 (
8.4
Ratio and Root Tests
Aim:
Ratio test
Root test
8.4.1
Ratio Test
Theorem 1. Let cfw_an be a positive sequence with lim
n
1. If L < 1, then
an+1
= L.
an
an converges;
n=1
2. If L > 1, then
an div
9 Curves in the Plane
9.2
Parametric Equations
Aim:
Convert between parametric equations and cartisian equations
9.2.1
Definitions
Definition 1. Let f and g be continuous functions on an interval I.