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đề thi giải tích cuối kỳ, Exams of Mathematical Analysis

Hanoi University of Science (HUS)Mathematical Analysis

đề thi cuối kỳ môn giải tich 2

Typology: Exams

2022/2023

Uploaded on 12/27/2024

10-trong-hieu
10-trong-hieu 🇻🇳

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DAI HOC QUOC GIA HA NOI DE THI CUOI HOC KY II Truong Dai hoc Khoa hoc Ty nhién NAM HOC 2022-2023 ——— —o0Oo—— Mén thi: Giai tich 2 Ma mén hoc: MAT2502 S6 tin chi: 4 Dé sé: Danh cho sinh vién khoa: K67 Nganh hoc: KHMT-TT & KHDL Thdi gian lam bai 120 phut (khéng ké thdi gian phat dé) Cau 1. Phat biéu dinh ly Cauchy-Hadamard dé tinh ban kinh hdi tu cua chudi ly thira. Tim ban kinh hdi tu va mién hdi tu cua chudi lay thira sau: co ar Lov n(Inn)2" Cau 2. Khai trién ham sé f(x) = sees thanh chudi lity thtra theo x. Cau 3. Phat biéu dinh nghia chudi Fourier. Khai trién ham sé f(x) = |sinx| thanh chudi Fourier trén doan [—7:, 7]. Cau 4. Cho ham sé a> Flay) = wip néu (x,y) 4 (0,0), 0, néu (x,y) = (0,0). (a) Tinh PHYA! PETC! Boo f(xy). (b) Khao sat tinh kha vi cla ham sé f(x,y) tai (0,0). Cau 5. Phat biéu dinh ly vé cong thitc tinh dao ham theo huéng. Tinh dao ham cé hudng ctia ham sé f (x,y,z) = e*+?¥+5 tai diém P(—2,2,—1) theo hudng cia vécto 3 = (<5 Ww 5) : Cau 6. Tim cuc tri tu do cua ham sé f(x,y) = xy— 2x8 —y?. Cha y: Thi sinh khong duoc sit dung bat cit tai liéu nao.