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MTH 229 Spring 2003 Common Final Exam: Mathematics Problems, Exams of Calculus

Wright State University (WSU) - DaytonCalculus

The final exam questions for a mathematics course (mth 229) from spring 2003. The exam covers various topics including differentiation, limits, calculus, and optimization. Students are required to use only a calculator and show their work for full credit. The exam consists of 9 problems with varying points assigned to each problem.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

koofers-user-uq3
koofers-user-uq3 🇺🇸

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MTH 229 COMMON FINAL EXAMINATION
Spring 2003
YOUR NAME: __________________________ INSTRUCTOR:__________________________
INSTRUCTIONS
1. Print your name and your instructor’s name on
this page using capital letters. Print your name
on each page of the exam. Do not separate the
pages of this exam.
2. This exam consists of this cover page and 8
additional pages containing 9 problems. Be
sure your exam is complete before beginning
work. Do not separate the pages of this exam.
3. Show your work. Work and/or explanation is
required on all problems unless otherwise
stated; if done well it may result in more credit.
Answers accompanied by insufficient, unclear,
or incorrect work may receive little or no credit.
4. The points assigned to a problem may not be
distributed equally among the parts of a
problem.
5. Do not use books, notes, papers, or other
references. You may use a TI-81 through TI-86
or equivalent calculator. You are NOT permitted
to use calculators capable of symbolic
differentiation or integration (such as the TI-89,
TI-92, or HP-48), portable computers, or any
other device capable of storing or receiving
information.
6. Do not submit scratch paper. Try to solve each
problem in the space provided. If you need
more space, use the back of this page or other
blank space. Be sure to tell on the original page
where your additional work can be found, and
begin your additional work with the number of
the problem being solved.
Problem 1
35
Problem 2
15
Problem 3
20
Problem 4
25
Problem 5
20
Problem 6
20
Problem 7
15
Problem 8
25
Problem 9
25
TOTAL
200
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Download MTH 229 Spring 2003 Common Final Exam: Mathematics Problems and more Exams Calculus in PDF only on Docsity!

MTH 229 COMMON FINAL EXAMINATION

Spring 2003

YOUR NAME: __________________________ INSTRUCTOR:__________________________

INSTRUCTIONS

  1. Print your name and your instructor’s name on this page using capital letters. Print your name on each page of the exam. Do not separate the pages of this exam.
  2. This exam consists of this cover page and 8 additional pages containing 9 problems. Be sure your exam is complete before beginning work. Do not separate the pages of this exam.
  3. Show your work. Work and/or explanation is required on all problems unless otherwise stated; if done well it may result in more credit. Answers accompanied by insufficient, unclear, or incorrect work may receive little or no credit.
  4. The points assigned to a problem may not be distributed equally among the parts of a problem.
  5. Do not use books, notes, papers, or other references. You may use a TI-81 through TI- or equivalent calculator. You are NOT permitted to use calculators capable of symbolic differentiation or integration (such as the TI-89, TI-92, or HP-48), portable computers, or any other device capable of storing or receiving information.
  6. Do not submit scratch paper. Try to solve each problem in the space provided. If you need more space, use the back of this page or other blank space. Be sure to tell on the original page where your additional work can be found, and begin your additional work with the number of the problem being solved.

Problem 1 35

Problem 2 15

Problem 3 20

Problem 4 25

Problem 5 20

Problem 6 20

Problem 7 15

Problem 8 25

Problem 9 25

TOTAL 200

(35) 1. Use the rules of differentiation to find the derivatives of the following functions. (a) † q ( u ) = cot( u ) a^2 + u^2 (b) † g ( x ) = x f ( x ) (treat † f ( x ) as an unknown function) (c) † r ( t ) = 4 sec^3 ( t ) (d) † k ( x ) = ln(sin( ax ) + cos( bx )) (e) † f ( x ) = tan-^1 ( x^1 /^3 ) (or † f ( x ) = arctan( x^1 /^3 ))

( 25 ) 4. Suppose † f ( x ) = x e -^ x^ (^2) / 2 . (a) Use calculus to find the intervals where † f ( x ) is increasing or decreasing, and the location of any local maxima or minima. (b) Use calculus to find the intervals where † f ( x ) is concave up or concave down, and the location of any inflection points. (c) Find the absolute maximum and minimum values on the interval [–2, 2].

( 20 ) 5. A rocket is launched vertically from a point on the ground. An observer, who is 1000 meters away from the base of the launching pad, notices that the angle of elevation of the rocket is increasing at a rate of π/40 radians per second when the angle of elevation is π/3. Find the speed of the rocket at that instant.

(15) 7. Following are some values of the function f ( x ). x 0.8 0.9 1.0 1.1 1. f(x) 0.437412 0.432777 0.420735 0.403261 0. (a) Use the values from the table to approximate † f ¢(0.9), † f ¢( 1 ), and † f ¢(1.1). Be sure to explicitly show the difference quotients you use. (b) Is f ( x ) concave up or concave down near x = 1? Explain your reasoning.

( 25 ) 8. A particle travels along a straight line. Its position at t seconds is given by † p ( t ) = t^3 - 6 t^2 + 9 t + 5 meters from a fixed origin on the line. (a) What is the average velocity of the particle during the interval 3 ≤ t ≤ 5? (b) What is the instantaneous velocity at t = 3 seconds? (c) What is the acceleration at t = 3 seconds? Is the particle speeding up or slowing down? (d) Find the total distance traveled during the interval † 0 £ t £ 5.