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METU NCC Mat 120 Spring 2010 Midterm 1

# METU NCC Mat 120 Spring 2010 Midterm 1 - M E T U Northern...

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Unformatted text preview: M E T U Northern Cyprus Campus Calculus for Functions of Several Variables I. Midterm Last Namei 3 Name 3 Student Department: Section: Signature: 6 QUESTIONS ON 7 PAGES TOTAL 100 POINTS Code 1 Math 120 ‘ Acad.Yeari 2009—2010 Semester 1 Spring Date : 27.3.2010 Time 3 9:00 Duration 3 120 minutes 1. (5+5+5:15 pts.) Determine Whether the following sequences converge or diverge. Find the limits of the ones which converge. sinn an : an+2 2. (8 pts.) Say an“ : for n 2 1 and (11 = 10. (a) Show that {an} is bounded below. «8 LL. ’w is decreasing. (b) Show that {an} § ‘ . « ‘W‘i’ﬁ *w “E r Qimk Wm .z s g 7 "a: Aw-hxmaasewtakimﬁt‘ﬁéﬁﬁwﬁg'aynm’5" 1 mg“ (91’ 3. (5+5+5+5+5=25 pts.) Determine whether the following series converge or diverge (Specify Clearly the method/ test used, and give details). § wxwmwm m “Mfume-e V “.muquam mayrwmm» 4mme¢ {)0 TI, : (arias: W, we“:er z» 1 1 ‘/1+——1/1——. 1 n n , .szmmwwg. ,.,\- M XNM‘ALW § m?“ kw 2 aim“; w a n (damn). : i 15‘ m»; m 4. (12 pts.) Find the radius and the interval of convergence of the power series 00 2"(2;c ~ 3)“ §w¢hnw§sﬁiv§> 6”“; 5 \. P k _ % x 7/ '1 Mm wwmm 'AVJ'4J’F/ur‘v‘ 5. 5+5+5+5+5225 pts.) Find the following power series expansions: 23”" d 0 (a) aroun a— . around a, : O. A“; ,7 WWW?” «A yxmx-wgmm E i ~ \ «a' (d) sing: around a = 7r. i mama “w a“. «ya-«x ~ 1 V1 —\$2 6. (15 pts.) Find the power series expansion of around a 2 0, and write the ﬁrst three nonzero terms explicitly. ‘ i 1 V1 —\$2 d3: : arcsint to ﬁnd the power series expansion of arcsinrc t (b) Use the relation / 0 around a 2 O. xtVémAuacpthqx-ﬁx we ...
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METU NCC Mat 120 Spring 2010 Midterm 1 - M E T U Northern...

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