METU NCC Mat 120 Spring 2009 Midterm 1

METU NCC Mat 120 Spring 2009 Midterm 1 - Dept/Sec Time...

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Unformatted text preview: Dept./Sec. Time Duration Signature : : : : : : Last Name Name Student No M E T U Northern Cyprus Campus Math 120 Calculus for functions of several variables I. Exam 23.03.2009 17: 40 120 minutes 7 QUESTIONS ON 7 PAGES TOTAL 100 POINTS 1 2 3 4 5 6 7 Q1 (16=4+4+4+4 pts.) Determine whether the following sequences converge or diverge, and find their limits if they converge. Explain your answers. (a) a n = √ n 2 + 1- n (b) b n = ln(2 n ) ln(3 n ) (c) c n = (- 1) n n n + 1 (d) d n = sin( √ n ) n Q2 (15=5+5+5 pts.) Determine whether the following series converge or diverge. Explain your answers. (a) ∞ ∑ n =1 sin(2 n ) n 2 + 2 n (b) ∞ ∑ n =1 cos( nπ ) n (c) ∞ ∑ n =1 sin ( 1 n ) n . Q3 (14=7+7 pts.) Computing the N-th partial sum s n = N ∑ n =1 a n of the following series, find their exact values ∞ ∑ n =1 a n if they converge. (a) ∞ ∑ n =1 parenleftbigg sin parenleftBig nπ 2 parenrightBig- sin parenleftbigg ( n + 1) π 2 parenrightbiggparenrightbigg (b) ∞ ∑ n =1 parenleftbigg...
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METU NCC Mat 120 Spring 2009 Midterm 1 - Dept/Sec Time...

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