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KOC University - Calculus I Midterm II Exam December 2011, Exams of Calculus

Tamil Nadu Open UniversityCalculus

The instructions and problems for the calculus i midterm ii exam held at koc university on december 14, 2011. The exam covers topics such as limits, derivatives, and integrals. Calculators are not allowed, and students must explain their answers and show their work to receive full credit.

Typology: Exams

2012/2013

Uploaded on 03/21/2013

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KOC¸ UNIVERSITY
MATH 106 - CALCULUS I
Midterm II December 14, 2011
Duration of Exam: 90 minutes
INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking allowed. You must always explain your
answers and show your work to receive full credit. Use the back of these pages if nec-
essary. Print (use CAPITAL LETTERS) and sign your name, and indicate your
section below.
Surname, Name: —————————————————
Signature: ————————————————————
Section (Check One):
Section 1: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 12:30) —–
Section 2: E. S¸. Yazıcı(Mon-Wed-Fri 14:30) —–
Section 3: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 10:30) —–
Section 4: E. S¸. Yazıcı(Mon-Wed-Fri 11:30) —–
Section 5: T. Etg¨u (Tue-Thu 12:30) —–
PROBLEM POINTS SCORE
1 23
2 15
3 18
4 15
5 12
6 9
7 9
TOTAL 101
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KOC¸ UNIVERSITY

MATH 106 - CALCULUS I

Midterm II December 14, 2011

Duration of Exam: 90 minutes

INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.

No books, no notes, no questions and no talking allowed. You must always explain your answers and show your work to receive full credit. Use the back of these pages if nec- essary. Print (use CAPITAL LETTERS) and sign your name, and indicate your section below.

Surname, Name: —————————————————

Signature: ————————————————————

Section (Check One):

Section 1: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 12:30) —– Section 2: E. S¸. Yazıcı(Mon-Wed-Fri 14:30) —– Section 3: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 10:30) —– Section 4: E. S¸. Yazıcı(Mon-Wed-Fri 11:30) —– Section 5: T. Etg¨u (Tue-Thu 12:30) —–

PROBLEM POINTS SCORE

TOTAL 101

  1. Compute the limits in a and b. Specify any infinite limits.

a) (9 points) lim x→ 0

x^2

sin x x^5

b) (9 points) lim x→∞ (x + ex)^1 /x^ =

c) (5 points) If the linearization of f (x) at x=0 is L(x) = ax + b, find lim x→ 0

2 f (x) ax + b

  1. (18 points) Sketch the graph of a function f satisfying the following properties. Identify local maximum, local minimum and inflection points on the graph, if they exist.
    • domain(f )= R \ { 3 }, f is twice differentiable on its domain.
    • lim x→ 3 −^

f (x) = −∞, lim x→ 3 +^

f (x) = +∞

  • lim x→−∞ f (x) = 1, lim x→+∞ f (x) = − 2
  • f ′(x) > 0 on (−∞, 1) and (5, ∞) f ′(x) < 0 on (1, 3) and (3, 5)
  • f ′′(x) > 0 on (−∞, 0) and (3, 7) f ′′(x) < 0 on (0, 3) and (7, ∞)
  1. (15 points) Find the critical points, the intervals where function is increasing and decreas- ing, local minimum, maximum and inflection points, if they exist and the intervals where the function is concave up and down for the function f (x) = x^2 /^3

2 −^ x

  1. (12 points) Find the absolute maximum and minimum values of f (x) =

x^2 + 4 2 x

on [1, ∞),

if they exist.