MATH 154 D100, Spring 2025 Midterm
Exam with Solutions
e3
March 17, 2025, 8:30–9:20am
SFU Email: @SFU.CA Signature:
Solutions
First
Name:
Last Name:
SFU ID #:
1. Using dark block letters, write your name, SFU student number and ID in the space provided.
2. This exam is 50 minutes long, and consists of 5 questions.
3. Write your solution in the space provided. If your answer continues elsewhere, indicate clearly (within
the space provided for the question) where your solution continues. A blank page for extra work is
provided after Question 4. You must cross out any work that you do not wish to be graded.
4. To receive full credit for a particular question, your solution must be complete and well-presented.
5. For the multiple choice questions, you must fill in the bubbles corresponding to your answers on the
final page. The corresponding multiple choice question number is indicated clearly in [square
brackets].
6. You may use a basic scientific calculator;mitted. You may leave answers as “calculator-ready”
expressions (such asprogrammable and graphing calculators ar3 + ln7 or epe2)not per-unless a decimal
value is specifically requested; however, answers should be simplified as far as is reasonable.
7. No books, notes, smartphones, electronic devices (other than your calculator), or any device capable of
connecting to the internet shall be within the reach of a student during the examination.
8. During the examination, copying from, communicating with, or deliberately exposing written papers
to the view of, other examinees is forbidden.
Question: 1 2 3 4 5 Total
, MATH 154 D100, Spring 2025
Midterm 3
Points: 6 9 9 6 10 40
SOME USEFUL FORMULAS
Change of Basis for Logarithms:
for any positive numbers a,b,x > 0.
Root-finding:
Starting from an initial value x0, successive iterates of Newton’s method (also called the Newton-Raphson
method) for finding a root of a differentiable function f are given by
L’Hospital’s Rule:
For a limit of a quotient with indeterminate form of type “0/0” or “1/1”, we have
.
Approximations:
The linearization L(x) (equivalently, tangent line approximation or first-degree Taylor approximation T1(x))
of the function f(x) about x = a is
L(x) = f(a) + f0(a)(x a).
The n-th degree Taylor polynomial of the function f(x) about x = a is
.
Exam with Solutions
e3
March 17, 2025, 8:30–9:20am
SFU Email: @SFU.CA Signature:
Solutions
First
Name:
Last Name:
SFU ID #:
1. Using dark block letters, write your name, SFU student number and ID in the space provided.
2. This exam is 50 minutes long, and consists of 5 questions.
3. Write your solution in the space provided. If your answer continues elsewhere, indicate clearly (within
the space provided for the question) where your solution continues. A blank page for extra work is
provided after Question 4. You must cross out any work that you do not wish to be graded.
4. To receive full credit for a particular question, your solution must be complete and well-presented.
5. For the multiple choice questions, you must fill in the bubbles corresponding to your answers on the
final page. The corresponding multiple choice question number is indicated clearly in [square
brackets].
6. You may use a basic scientific calculator;mitted. You may leave answers as “calculator-ready”
expressions (such asprogrammable and graphing calculators ar3 + ln7 or epe2)not per-unless a decimal
value is specifically requested; however, answers should be simplified as far as is reasonable.
7. No books, notes, smartphones, electronic devices (other than your calculator), or any device capable of
connecting to the internet shall be within the reach of a student during the examination.
8. During the examination, copying from, communicating with, or deliberately exposing written papers
to the view of, other examinees is forbidden.
Question: 1 2 3 4 5 Total
, MATH 154 D100, Spring 2025
Midterm 3
Points: 6 9 9 6 10 40
SOME USEFUL FORMULAS
Change of Basis for Logarithms:
for any positive numbers a,b,x > 0.
Root-finding:
Starting from an initial value x0, successive iterates of Newton’s method (also called the Newton-Raphson
method) for finding a root of a differentiable function f are given by
L’Hospital’s Rule:
For a limit of a quotient with indeterminate form of type “0/0” or “1/1”, we have
.
Approximations:
The linearization L(x) (equivalently, tangent line approximation or first-degree Taylor approximation T1(x))
of the function f(x) about x = a is
L(x) = f(a) + f0(a)(x a).
The n-th degree Taylor polynomial of the function f(x) about x = a is
.
