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英語 高校生

分かる方教えてください🙇‍♂️

26 1 Choose the best answer to fill in the blanks. (15) (1) Peter ( ) for ten years next month. 1 teaches 3 will teach (3) Our teacher is ( likely (2) In my class, there are three students from abroad. One is from England and ( are from Australia. 1 another (4) My father is ( 1 more tall 2 others (5) My parents objected ( 1 to my climbing 3 me to climbing (8) ( (6) She had to shout to make herself ( 2 hear 1 have heard 1 Judging from 3 Though 2 will be teaching 4 will have taught ) to come by the time we promised to get together. 2 possible 3 probable 4 definite ) of the two men standing at the gate. 2 taller 3 the tall 3 the other (7) The project could be called a success, all things ( 11 consider 2 considered 3 considering ) the mountain alone in winter. 2 me of climbing 4 on me to climb TOT ) the sky, it will rain this afternoon. (10) We are now in the ( 1 late ). 3 heard (11) All teachers and students are not ( 1 necessarily 2 necessary 4 the others ) half of our training camp. 3 later 2 latter 4 the taller (9) You must leave now; ( ), you will be late for your social studies class. 1 instead 2 therefore 3 otherwise 4 accordingly 4 hearing 2 Generally speaking 4 It being 4 to consider (13) Next week's seminar ought to provide ( 1 ours (2) our 4 last ) wise and hardworking. 3 need 4 needed (12) ( ) had the war begun when terrorists hijacked a plane. 1 The moment 2 No wonder 3 Hardly 4 As soon as /13 ) with a lot of new information. 3 ourselves 4 us made er discr deceived ( 東京電機大 ) Intentio e you go prepare e two g notice (京都産業大) (関西学院大 ) THIOS (千葉工業大) Gs not lil aimless NT 13 (実践女子大) (摂南大) (大阪学院大 ) chance (國學院大) (二松学舎大 SE 否定 not alwa not quit けではな • I not at (センター試験) lot ~ ei •I (城西大 N 全体否定 I する ardly N SOO A

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数学 高校生

極限の問題です。 ⑴が分かりません。なぜ範囲が「-π/4<θ/2^(k+1)<π/4」と言えるのでしょうか?

& 8 数列の極限 / 漸化式 x<0 とするとき, 次の条件によって定められる数列{an}がある. (n=1,2,3, ......) (3) n10 表せ. ak+1= 2"×sin a1 cos 0 an = COS が成り立つことを示せ. 2n が成り立つことを証明せよ. (3) bn=axax as ×・・ π 0 <. 4 2k+1 Cn+1=2"x2sin 2ntr =2" x sin lib=lim 0 2 an+1= 解答量 (1) 数学的帰納法で示す. n=1のとき成り立つ. n=kで成り立つとすると, 1/(1+(n)=1/(1+ T Cn=2"sin- 0 2n 半角の公式を連想する 本問は三角関数がらみである. そこで与えられた漸化式を三角関数の公式 と関連させて眺めよう. すると, cos 0 = 2 0 X cos X cos 2 0 2n 0 2n 1+an 2 22 0 0 Cm は一定で, C=C=2cos sin 2 2 1+cos であるから, cos ......Xan (n=1, 2, 3, ..... とおく.0=0のとき, limb を0を用いて n→∞0⁰ (新潟大・理,医,歯) 0 22 X cos -X cos 2 n-∞ sin (0/2") 0 X cos 0 2k 0 2k+1 = ->0 よって,n=k+1でも成り立つから,数学的帰納法により証明された. (2) 与式の左辺をcm とおくと, ədalə 0 (aimagenranspot.come on COS 2n+1 2n+1 2 X cos X cos =sin( 23 X...... X cos nail 1+cos 0 2 COS .. ayaz......an ... sin0=2"sin 0/2" sin sin 0 0 22 0 2n 2 0 2k+1 X cos = sin (n=1, 2, 3, ………….) 0 2n 0 2n ak+1=COS の公式を連想するのは難しくはないだろう. X・・・・・・ X cos Cn -bn 0 2k+1 0 2n 1 (1+cosa) = cos2mm 2 √ x2 = |X|に注意して√を外 す。 ← (2) も数学的帰納法で示すこと ができる. 0 2n+1 (2sinacosa=sin2a) ←2sin COS 0 2n 0 2n+1 Cn+1=2x5in274 =sin 0 2n "xsin ni xcus=xcus=-=+=+= 1 x ... x cos x cus int →0 (n→∞)

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