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Specify - Calculus One - Exam, Exams of Calculus

Tamil Nadu Open UniversityCalculus

Key points of this exam are: Specify, Limits, Infinite Limits, Compute, Piecewise, Defined Function, Continuous, Real Numbers, Positive Real Number, Solution

Typology: Exams

2012/2013

Uploaded on 03/21/2013

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KOC¸ UNIVERSITY
MATH 106 - CALCULUS I
Midterm I November 16, 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 24
2 8
3 10
4 16
5 10
6 17
7 10
8 7
TOTAL 102
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KOC¸ UNIVERSITY

MATH 106 - CALCULUS I

Midterm I November 16, 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 102

  1. Compute the following limits. Specify any infinite limits.

a) (8 points) lim x→ 1

x^3 − 1 x^2 − 1

b) (8 points) (^) xlim→ 3 −

x − 2 |x − 3 |

c) (8 points) (^) x→−∞lim x +

x^2 − 4 x + 1 =

  1. a) (6 points) Write the precise definition of limx→a f (x) = L. (ϵ,δ definition of limit)

b) (10 points) Prove that lim x→ 0 x cos(1/x) = 0 by using the ϵ,δ definition of limit.

(Hint: | cos(1/x)| ≤ 1 )

  1. (10 points) Evaluate lim θ→ 0

esin^ θ^ − 1 θ

  1. Differentiate the following functions.

a) (9 points) g(t) =

t cos(t^4 )

b) (8 points) f (x) =

x

)√x