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