The University of British Columbia
Midterm Examination - October 14, 2011
MATH 104, Section 105
Closed book examination Time: 50 minutes
Last Name First ‘MLLCLQ;
Signature W7
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Student Number ‘
Special Instructions:
No memory aids are allowed. , i ' . ,

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Final Answers
MATH104 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

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ti
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Final Answers
MATH104 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

Assignment 5
1. Consider the curve 2x3 y + xy 2 = 8. Determine the equation of the tangent line to the
curve at the point (1, 2) . Find y .
Solution. Dierentiating the equation with respect to x, we nd
6x2 y + 2x3 y + y 2 + 2xyy = 0.
(1)
So at the point (

Problems in Continuity and Dierentiability;
Derivatives as rate of change; Deriving functions
SOLUTION
1. Find the number c that makes
x c , if x 0
f (x) = c + 1
x2 + c, if x > 0
continuous for every x.
Solution:
Note that f (x) is continuous for every x

Assignment 6 SOLUTIONS
1. In the year 2000, a student takes out a 20000 dollars loan at an annual interest rate of
r (interest compounded continuously). The student makes one loan payment of 10000
dollars in 2015, then one more loan payment of L in 2020 a

Midterm 1
Math 184 Fall 2011
0 N0 calculators, cell phones, formula sheets (etc) are permitted.
0 This exam has 8 pages, including this cowrr page and the scrap paper page.
Make sure you have all 8 pages.
0 Show all your work — a correct answer will recei

Midterm 1
Math 184 Fall 2011
o No calculators, cell phones, formula sheets (etc) are permitted.
0 This exam has 8 pages, including this cover page and the scrap paper page.
Make sure you have all 8 pages.
0 Show all your work — a correct answer will recei

1
Calculus 104 Section 104
Name/ID:
October 13 2011
Guillermo Mantilla
Midterm I
Instructions: Time 80mins. No books, no notes, no calculators, no cell phones, no pagers,
no electronic devices of any kind. PUT YOUR ANSWER IN THE BOX PROVIDED.
Show every s

The University of British Columbia
Midterm Examination - October 14, 2011
MATH 104, Section 105
Closed book examination
Time: 50 minutes
Last Name
First
Signature
Student Number
Special Instructions:
No memory aids are allowed. Show all your work; little

Sample for Test 1
Math 13-4 — ZDIIW Term 2 — 3 Feb EUlﬂ
Section 2131 {Warren Code]
Last Name:
First Name:
Student Numb er:
Read all of the following information before starting the exam:
1 This is a sample for Test 1, but these directions are as the},r

THE UNIVERSITY OF BRITISH COLUMBIA
MATH 104 (106)
Midterm 1
13 October 2011
FULL NAME: L STUDENT # ;
SIGNATURE:
TIME: 80 MINUTES
This Examination paper consists of 8 pages (including this one). Make sure you have all 8.
INSTRUCTIONS:
N 0 memory aids a

Sample for Test 1
Math 184 - 2011W Term 2 - 3 Feb 2012
Section 201 (Warren Code)
Last Name:
First Name:
Student Number:
Read all of the following information before starting the exam:
This is a sample for Test 1, but these directions are as they will app

The University of British Columbia
Midterm Examination - October 14, 2011
MATH 104 Section 102
Closed book examination
Last Name
Time: 50 minutes
Signature
Student Number
Special Instructions:
No memory aids or calculators are allowed. Show all yo

Assignment 8
1. (i) Suppose f is a function dened on an interval I. If f (x) is positive for all x in I,
what can you conclude about the behaviour of f on I?
Answer. f is strictly increasing on I.
(ii) Let f be dened on an interval I with an interior poin

Assignment 10
November 29, 2013
1. Use linear approximation and quadratic approximation to approximate 631/3 .
Answer. Notice that 641/3 = 4. We use the function f (x) = x1/3 and choose the center
a = 64. Then by linear approximation,
631/3 = f (63) f (64