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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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数学 高校生

高認の問題です。③はなぜ「〜できますか?」で「shall i〜?」なんですか?調べてもわからなかったので教えてください。

を答え (電話での会話) (平成26年11月問題2) こ A: Hello, This is Ted Brennan. Can I speak to Mr. Nelson? B: I'm sorry. He'll be out of the office until three o'clock. A: Well, [ ] B: Hold on, please. I'll get something to write with. ① do you know when he'll come back? ② will you call him back later? 3 shall I talk to him soon? ④ can I leave amessage? Hold on (電話機を切らずに)そのままお待ち下さい。 / write with (A)~で書く、(A)にはベ か万年筆か鉛筆が入る。Something to write with 何か (それで) 書くもの / call back (電話で)返 の電話をかける。 /message [ メッセージ] 伝言、 メッセージ でんごん A:もしもし、こちらはテッド・ブレナンですが。ネルソンさんいらっしゃいますか 訳 : 私はネルソンさんとお話できますか) ? B : あいにくです。 彼は3時まで会社を出ております。 A : それじゃ [] B:電話を切らないで下さい。 何か書くもの (ペンか鉛筆) を取ってきますので。 ① いつ戻ってらっしゃるかご存知ですか? ぞんじ ② ではネルソンさんに電話を下さるようにお伝えください。 ③ もうすぐ彼と話ができますか? ④ それでは(彼への)伝言 (でんごん、メッセージ)を残しておくことができますか? 正解は④、 “leave” には 「残す」 と「(町、国から) 離れる」 の二つの意味がある。 (A++h M

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数学 高校生

英語の長文ってどうやったら読めるようになりますか

1 次の英文を読んで、問 (1) ~ (5) に且本語で答えなさい。 Lobola is the African custom of paying fora bride. Although it is an old custom, not In fact, it is being debated in Botswana. everyone in African cultures is happy with it. Many people, including many women, support payment of lobola. They explain that in Tswana culture, a marriage means joining a family, not just marrying an individual. The idea of marrying into a family is very African. just the man.Through marriage, the young woman's family loses their daughter as she then becomes a part of her husband's family. Lobola is a way to show thanks. It is a form of generosity in African culture. In its traditional form, they also explain, the groom's family gave cattle to the bride's family. But it didn't matter whether the family owned cattle or not. A woman does not get married to A man only had to pay what he could afford if he had no cattle, he could give something else, even the smallest form of payment. The tradition of lobola was a matter of pride. Today, lobola is often given in cash. purchase of a bride. Lobola is meant to join two families together. They know that But its supporters say it is not about the some people abuse the custom. But they believe that the tradition should not be tossed out because it has many positive effects. Rather than get rid of it, many believe it should just be explained better. However, many others say this custom should be stopped. They think it has become commercialized. Families make lots of demands on the groom. They think this makes lobola look very bad. They argue that in Africa's past, a girl was an asset at home. and other household chores. She did the cooking When a family lost that child through marriage, it demanded payment. Today, they think that lobola has changed into a useless tradition. In this custom, a man is buying the right to control a woman. They say women are individuals with rights. In today's world, parents do not have to be paid for a bride because their male and female children are equal. They all work and make contributions to the household. They believe that paying lobola makes it seem like a man is buying a pair of shoes or a bicycle, instead of getting married. They also argue that it is often a financial burden for couples. It is too difficult for many people to pay the price asked. So, is lobola a rich tradition, bringing families together? Or is it an ugly custom of buying women? This debate continues in Botswana, as does the custom.

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