Continuous - Calculus - Exam, Exams of Calculus

Main points of this exam paper are: Continuous, Value, Tangent Line, Graph, Limit, Integral, Area, Region Bounded, Curves, Improper Integral

Typology: Exams

2012/2013

Uploaded on 03/21/2013

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KOC¸ UNIVERSITY
MATH 102 - CALCULUS
Final Exam June 6, 2005
Duration of Exam: 120 minutes
INSTRUCTIONS: No calculators may be used on the test. No books, no notes, no questions,
and talking allowed. You must always explain your answers and show your work to receive full
credit. Use the back of these pages if necessary. Print (use CAPITAL LETTERS) and sign
your name, and indicate your section below. GOOD LUCK!
Surname, Name: ————————————————–
Student ID no: —————————————————–
Signature: ————————————————————
Section (Check One):
Section 1 (Vahap Erdo˘gdu) : —–
Section 2 (Burak ¨
Ozba˘gcı- MW: 11:30-13:20): —–
Section 3 ( ¨
Ozg¨ur M¨ustecaplıo˘glu): —–
Section 4 (Tolga Etg¨u - MW: 9:30-11:20): —–
Section 5 (Tolga Etg¨u - MW: 12:30-14:20): —–
Section 6 (Burak ¨
Ozba˘gcı- MW: 14:30-16:20) : —–
PROBLEM 123456789TOTAL
POINTS 10 10 10 10 10 10 10 20 10 100
SCORE
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KOC¸ UNIVERSITY

MATH 102 - CALCULUS

Final Exam June 6, 2005

Duration of Exam: 120 minutes

and talking allowed. You must always^ INSTRUCTIONS:^ No calculators may be used on the test. No books, no notes, no questions, explain your answers and show your work to receive full credityour name, and indicate your section below. GOOD LUCK!. Use the back of these pages if necessary. Print (use CAPITAL LETTERS) and sign

Surname, Name: ————————————————– Student ID no: —————————————————– Signature: ————————————————————

Section (Check One):

Section 1 (Vahap Erdo˘Section 2 (Burak Ozba˘¨ gdu) :gcı- MW: 11:30-13:20): —–—– Section 3 ( Section 4 (Tolga Etg¨Ozg¨¨ ur M¨ustecaplıo˘u - MW: 9:30-11:20):glu): —–—– Section 5 (Tolga Etg¨Section 6 (Burak Ozba˘¨ u - MW: 12:30-14:20):gcı- MW: 14:30-16:20) : —–—–

PROBLEM 1 2 3 4 5 6 7 8 9 TOTAL POINTS 10 10 10 10 10 10 10 20 10 100 SCORE

Problem 1 (10 pts) Let

f (x) =

{ (^) arctan( 1 a + x^ x )^ , x >, x ≤^ 0; 0. Find the value for a that will make f continuous.

Problem 2 (10 pts) Find the tangent line to the graph of

f (x) =

∫ (^) x 2 0

√1 + t (^3) dt

at x = √2.

Problem 5 (10 pts) Evaluate the following integral. ∫ (^1) 0 x

(^2) ex (^) dx

Problem 6 (10 pts) Find the area of the region bounded by the curves y = x^2 − 2 and y = −|x|.

(8.b) (5 pts) (^) ∑∞

n=

cos( n^1 )

(8.c) (10 pts) (^) ∑∞

n=

2 nn!n! (2n)!

Problem 9 (10 pts) Find the radius of convergence and the interval of convergence of the following power series.

∑^ ∞ n=

√^ xn n 3 n