Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
MATH 100, Section 921
Final Examination June 25, 2015
Page 1 of 17
Final Examination
Duration: 2.5 hours
This test has 8 questions on 17 pages, for a total of 106 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are shortansw
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Final Answers
MATH100 December 2012
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. For your grading
you can get the full solutions here.
If youre not quite ready
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
Check if f = is‘giﬁgumﬂabliat ac = 0. How about other values of an?
wagg? $wd' .¥‘(cb <3A€§5_
,_ Um «"170.
44 {RO Find the derivative of f = ﬂ using the deﬁnition of the derivative.
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f (X): {T70 ( )
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um Na “K
,— \’\
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
1. Compute
, m5+m4+m3+$2+w+1
11ml ——+1——
—>— ~ » V
m 3: ‘~/\ B’L \QNC {3H4 .‘.»\QN\
2. Compute \B
m16+w12—w4——1
lim ——
93—)1 3:8 — ]_
3. Two horses start a race at the same time and ﬁnish in a tie. Prove that at some
/ \
time during the race they have t
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
(a) Determine
_ 23:
km
rte—+0 tan(:1:)
7 ~
(b) What is the domain of f(a:) = \/d;2 — 91: L )0”le
(c) Simplify log2(64). j: 5 Q]
(1) Let f 2 4x2. Find f’ using the deﬁnition of the derivative.
. Consider the equation
1w2=l USr/LVT
1r
Show that this e
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
1. Compute
x5 + x 4 + x3 + x 2 + x + 1
x1
x+1
lim
2. Compute
x16 + x12 x4 1
x1
x8 1
lim
3. Two horses start a race at the same time and nish in a tie. Prove that at some
time during the race they have the same speed.
4. Suppose g(x) is a function that is
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
1. Find the degree 7 Taylor polynomial of f = sin(a:) about :1: : 7r/2. Bonus
question: Can you write down the general degree 77. Taylor polynomial?
2. Find the degree 3 Maclaurin polynomial of
(a) f(m) = 5 + 3x — 2x2
T560: 5 4 7>< ~le
(b) g(a:) = 5 + 39:
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
1. Find the degree 7 Taylor polynomial of f (x) = sin(x) about x = /2. Bonus
question: Can you write down the general degree n Taylor polynomial?
2. Find the degree 3 Maclaurin polynomial of
(a) f (x) = 5 + 3x 2x2
(b) g(x) = 5 + 3x 2x2 + 10x7
(c) What do
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
1. (a) Determine
2x
x0 tan(x)
(b) What is the domain of f (x) = x2 9?
lim
(c) Simplify log2 (64).
(d) Let f (x) = 4x2 . Find f (x) using the denition of the derivative.
2. Consider the equation
1
x
Show that this equation has a negative solution.
3. Find
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
Find constants co and 01 so that the line y = Co + C13: is the line of best ﬁt to the
function f = ea” at 112': 0.
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Lk \'\<7\V'L gvotVWWXA [\M‘fwa.
Chose Y0: b \ S6 {(0): it {We}: Eye: {L
y t. = X
'3: >< +4 Find constants c0, c
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
MATH 100 FINAL EXAM PRACTICE PROBLEMS
After doing the past exams you should tackle all of these extra review problems.
Question 1: Short answer questions.
Evaluate the following limits without using LHpitals Rule, if they exist:
o
x+3
. (Answer: DNE)
x2 x
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
Math 100(001), Review Questions for Final Exam (A)
Total 116
PART I: There are 3 multiple choice questions. Circle the correct answer.
Each question is 3 marks. No partial marks. Total of 9 marks.
ea: _ e2:1:
1. Whatis lim
mmo. 32$
?
if ~\ 3L l~ vl
(b
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
University of British Columbia Okanagan
Math 100(001), Test 1
Sep. 29, 2011 Time: 50 minutes Instructor: Javad Tavakoli
' Total 24 points
Name 8: student #:
PART I: There are 3 multiple choice questions. Circle the correct answer.
Each question is 3 m
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Final Answers
MATH100 December 2011
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. For your grading
you can get the full solutions here.
If youre not quite ready
Full Solutions
MATH100 December 2013
April 16, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite
s
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w
ns
la
na
Fi
ti
rip
sc
n
Final Answers
MATH100 December 2010
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. For your grading
you can get the full solutions here.
If youre not quite ready
Full Solutions
MATH100 December 2014
April 22, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite
Mathematics 100201
Page 1 of 6
StudentNo.:
Midterm 1
Duration: 50 minutes
This test has 5 questions on 6 pages, for a total of 40 points.
Read all the questions carefully before starting to work.
Q1 and Q2 are shortanswer questions; put your answer i
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Winter 2015
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Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Winter 2015
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Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Summer 2015
cow)
Review Questions for MATH 100 Final Exam Page 1
(Ayge Alaca)
' _ a:
1. Find Hm Ml.
:cvO 3:2
2. Find lim acem.
mwo
3. Find lim "4h"2?
h»o h
4. Find the inverse of the function y = 1n(39: + 1).
5. Find the equation of the tangent line to the curve 11:
Differential Calculus with Applications to Physical Sciences and Engineering
MATH 100

Fall 2006
Full Solutions
MATH100 December 2013
December 4, 2014
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not qui