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Number - Mathematics - Exam, Exams of Mathematics

Acharya Nagarjuna UniversityMathematics

This is the Exam of Mathematics which includes Plane Parallel, Specific Heat, Perpendicular, Unit Tangent Vector, Parametric Equations, Vector Parallel, Parameterization, Curve, Intersection etc. Key important points are:Number, Provided, Accompanying, Continuous, Evaluate, Money, Account, Money to Triple, Compounded, Interest

Typology: Exams

2012/2013

Uploaded on 02/21/2013

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The University of British Columbia
Final Examination - December 16, 2006
Mathematics 104/184
All Sections
Closed book examination Time: 2.5 hours
Last Name First Signature
Student Number
Special Instructions:
No books, notes, or calculators are allowed. Unless it is otherwise specified, answers may
be left in “calculator-ready” form, where calculator means basic scientific calculator. Show
all your work, little or no credit will be given for a numerical answer without the correct
accompanying work. If you need more space than the space provided, use the back of the
previous page. Where boxes are provided for answers, put your final answers in them.
Rules governing examinations
•Each candidate must be prepared to produce, upon request, a
UBCcard for identification.
•Candidates are not permitted to ask questions of the invigilators,
except in cases of supposed errors or ambiguities in examination
questions.
•No candidate shall be permitted to enter the examination room
after the expiration of one-half hour from the scheduled starting
time, or to leave during the first half hour of the examination.
•Candidates suspected of any of the following, or similar, dishon-
est practices shall be immediately dismissed from the examination
and shall be liable to disciplinary action.
(a) Having at the place of writing any books, pap ers
or memoranda, calculators, computers, sound or image play-
ers/recorders/transmitters (including telephones), or other mem-
ory aid devices, other than those authorized by the examiners.
(b) Speaking or communicating with other candidates.
(c) Purposely exposing written papers to the view of other can-
didates or imaging devices. The plea of accident or forgetfulness
shall not be received.
•Candidates must not destroy or mutilate any examination mate-
rial; must hand in all examination papers; and must not take any
examination material from the examination room without permis-
sion of the invigilator.
•Candidates must follow any additional examination rules or di-
rections communicated by the instructor or invigilator.
1 42
2 10
3 12
4 12
5 12
6 12
Total 100
Page 1 of 10 pages
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Download Number - Mathematics - Exam and more Exams Mathematics in PDF only on Docsity!

The University of British Columbia Final Examination - December 16, 2006 Mathematics 104/ All Sections

Closed book examination Time: 2.5 hours

Last Name First Signature

Student Number

Special Instructions:

No books, notes, or calculators are allowed. Unless it is otherwise specified, answers may be left in “calculator-ready” form, where calculator means basic scientific calculator. Show all your work, little or no credit will be given for a numerical answer without the correct accompanying work. If you need more space than the space provided, use the back of the previous page. Where boxes are provided for answers, put your final answers in them.

Rules governing examinations

  • Each candidate must be prepared to produce, upon request, a UBCcard for identification.
  • Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambiguities in examination questions.
  • No candidate shall be permitted to enter the examination room after the expiration of one-half hour from the scheduled starting time, or to leave during the first half hour of the examination.
  • Candidates suspected of any of the following, or similar, dishon- est practices shall be immediately dismissed from the examination and shall be liable to disciplinary action. (a) Having at the place of writing any books, papers or memoranda, calculators, computers, sound or image play- ers/recorders/transmitters (including telephones), or other mem- ory aid devices, other than those authorized by the examiners. (b) Speaking or communicating with other candidates. (c) Purposely exposing written papers to the view of other can- didates or imaging devices. The plea of accident or forgetfulness shall not be received.
  • Candidates must not destroy or mutilate any examination mate- rial; must hand in all examination papers; and must not take any examination material from the examination room without permis- sion of the invigilator.
  • Candidates must follow any additional examination rules or di- rections communicated by the instructor or invigilator.

Total 100

Page 1 of 10 pages

[42] 1. Short Problems. Each question is worth 3 points. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work.

(a) Find the number c that makes

f (x) =

x^2 − 3 x − 10 x + 2

if x 6 = − 2 c if x = − 2

continuous for every x.

Answer:

(b) Evaluate lim t→ 0

t + 9 − 3 √ t

Answer:

(c) Evaluate lim h→ 0

(h + 3)^2 − 9 (h − 5)^2 − 25

Answer:

(d) If you put money in an account that pays 6% interest, compounded continuously, how long will it take for your money to triple?

Answer:

(i) Let y = y(x) be the function defined implicitly by the equation y + ln(y + 3) = x^2. Find dy dx

in terms of x and y.

Answer:

(j) Determine where the function

f (x) =

1 + ln(x + 1) x + 1

, x > − 1

is increasing.

Answer:

(k) Determine where the function f (x) =

x x + 2

, x 6 = −2, is concave down.

Answer:

(l) Find the global minimum of the function f (x) =

x x^2 + 4

over the interval [− 1 , 5].

Answer:

(m) Determine the sum − 4

Answer:

(n) Let c 0 + c 1 x + c 2 x^2 +... be the Taylor Series of the function f (x) = (x + 1)e−x^ at a = 0. Determine the value of c 2.

Answer:

[12] 3. Suppose that when a busy restaurant charges $7 for its tomato appetizer, an average of 60 people order the dish each night. When it drops the price of the appetizer to $5, the number ordering it rises to 66. Assume that the demand q is a linear function of the price p. If each appetizer costs the restaurant $3 to make, use calculus to find the price it should charge to maximize its profit from the appetizer. You do not need to justify that your answer provides the maximum profit.

[12] 4. Let y = f (x) =

2 x x^2 + 1

(a) Find the interval or intervals on which f (x) is increasing. [3pts]

(b) Find the interval or intervals on which f (x) is concave up. [3pts]

(c) Sketch the graph of y = f (x), and indicate the x-coordinates of any inflection points, and the values of x where any global maxima or global minima occur. (Hint:

[6pts]

[12] 6. The price p (in dollars) and demand q for a product are related by

p^2 + 2q^2 = 1100.

If the price is increasing at a rate of $2 per month when the price is $30, find the rate of change of the revenue in dollars per month.

The End