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Value Problem - Calculus for the Biological Sciences - Exam, Exams of Calculus

Amity University - BiharCalculus

This is the Exam of Calculus for the Biological Sciences which includes Value Problem, Initial, Substitution, Antiderivatives, Rewriting The Integrand, Propelled, Least One Number, Boxes etc. Key important points are: Value Problem, Initial, Metapopulation, Species, Patches Occupied, Equilibria, Graphically, Eigenvalue Method, Stability, Extinct

Typology: Exams

2012/2013

Uploaded on 02/18/2013

aishwaryai
aishwaryai 🇮🇳

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SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Instructor: A. Wise
Midterm 2
MATH 155
July 14th, 2003, 8:30-9:20am
Name: (please print)
family name given name
Signature:
INSTRUCTIONS
1. DO NOT OPEN THIS BOOKLET UNTIL TOLD TO DO SO.
2. Write your name above in block letters and sign below your name.
Write your student number and your family name in the boxes on the back page.
3. For each question write your final answer in the box when one is provided. You
must show all your work when space is provided. If this space is insufficient you
may use the back of the previous page.
4. This exam contains this cover page, the normal distribution table, two formula
sheets and 7 pages with a total of 6 questions. Once the exam begins please
check to make sure your exam is complete with a total of 11 pages.
5. No book, paper, or device, other than the usual writing instruments and this
booklet, shall be within reach of a student during the examination. In particular,
no calculators are allowed.
6. During the examination, speaking to, communicating with, or
exposing written papers to the view of, other examinees is forbidden.
7. Students observed writing anything after the call to stop writing will
be subject to summary penalties.
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Download Value Problem - Calculus for the Biological Sciences - Exam and more Exams Calculus in PDF only on Docsity!

SIMON FRASER UNIVERSITY

DEPARTMENT OF MATHEMATICS

Instructor: A. Wise

Midterm 2

MATH 155

July 14th, 2003, 8:30-9:20am

Name: (please print) family name given name

Signature:

INSTRUCTIONS

1. DO NOT OPEN THIS BOOKLET UNTIL TOLD TO DO SO.

  1. Write your name above in block letters and sign below your name. Write your student number and your family name in the boxes on the back page.
  2. For each question write your final answer in the box when one is provided. You must show all your work when space is provided. If this space is insufficient you may use the back of the previous page.
  3. This exam contains this cover page, the normal distribution table, two formula sheets and 7 pages with a total of 6 questions. Once the exam begins please check to make sure your exam is complete with a total of 11 pages.
  4. No book, paper, or device, other than the usual writing instruments and this booklet, shall be within reach of a student during the examination. In particular, no calculators are allowed.
  5. During the examination, speaking to, communicating with, or exposing written papers to the view of, other examinees is forbidden.
  6. Students observed writing anything after the call to stop writing will be subject to summary penalties.

[5] 1. Solve the initial value problem

dy dx

= (y+1)^3 , with y(0) = 1.

ANSWER

SHOW YOUR WORK

2. Suppose we are studying a given species in a metapopulation using Levin’s model. That

is, the fraction of patches occupied by the species at time t, p(t), satisfies

dp dt

= 2p(1 − p) − p for t ≥ 0.

[4] (a) Find all equilibria of this model and dis- cuss their stability graphically or using the eigenvalue method.

ANSWER

SHOW YOUR WORK

[3] 3. (a) Find the Taylor Polynomial of degree

3 about x = 0 for f (x) = sin x.

ANSWER

SHOW YOUR WORK

[2] (b) Use your result in part (a) to approximate the

value of

√^1

. Leave the answer in unsimpli- fied numerical form.

ANSWER

SHOW YOUR WORK

[3] (c) Give an upper bound for the error of your ap- proximation using the formula

|Rn(x)| =

|f (n+1)(z)| (n + 1)!

|x − a|n+1.

Leave the answer in unsimplified numerical form

ANSWER

SHOW YOUR WORK

[5] 4. Suppose a variable X is normally distributed with mean

4 and standard deviation 2. Find the probability that the variable X assumes values greater than 2.

ANSWER

SHOW YOUR WORK:

[5] 6. State the reason(s) why the integral

∫ (^) π/ 2

−π/ 2

tan x dx is con- sidered improper. Does this integral converge or diverge? If it diverges explain why. If the integral converges find the value that it converges to. (You may refer to the formula sheet to obtain

tan x dx.)

ANSWER

SHOW YOUR WORK:

Student number

Family name

DO NOT WRITE BELOW THIS LINE

Question Maximum Score

Total 40