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数学 高校生

このページで言っているのは、適度に変形してから微分した方がよいということでしょうか?1番左上に、対数微分法の利点と書いてありよく分からなくなってしまいました。

Play Back 対数微分法の利点と不等式の証明 探究例題 5 不等式の証明での工夫 次の問題について,太郎さんと花子さんと次郎さんが話している。 問題: eを自然対数の底, すなわち e = lim1+ 817 +1) とする。すべての正の 実数xに対し、不等式(1+1)* <e が成り立つことを示せ。 (東京大改) 太郎: (右辺) - (左辺)=f(x) とおいて,微分すれば簡単そうだよ。 x f(x)=e-(1+1/2) とおくと, f(x) =・・・あれ? x ... 花子:(1+1/2) はそのままだと微分できないね。(関数) (M) のような形を微分する ときは、対数微分法を利用したよね。 太郎:なるほど。f(x)=e-(1+1/2) 2 の両辺の対数をとればよいかな。 次郎 : それだと, 対数微分法はうまくできないよ。 そもそも, lim 1+ x 1 817 =eより、 x→∞としたとき1+- の極限値はeとなるから,(1+1/2)がエン XC で単調増加することを示すことができればよいよね。 (次郎さんの解答) g(x) = 1+ +12) とおくと,x>0より g(x)>0であるから両辺の対数をと ると x logg(x)=log(1+1/2) ⇔logg(x) = x{log(x+1)-logx} 両辺をxで微分すると ... (A) 花子:対数をとるとよいということだね。 与えられた不等式を、対数をとって変形 してから考えるとどうなるかな。 (花子さんの解答〕 x>0より (1+1)>0であるから,(1+2) <e の両辺の対数をとると ⇔log(x+1)-logx- <0 ..① 10g(1+1/2) <1⇔x{log(x+1)-logx} <1 D (0 <) 18ol x 20 与えられた不等式と同値である① を示す。 ①の左辺をm(x) とおいて, m(x) を xで微分すると (B) (1) (A)に続くように,問題を解け。 (2) (B)に続くように,問題を解け。 (

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英語 中学生

(3)長文問題の一部です そのこと は、なぜ、The thingではなく、Thatなのですか? A. That makes the trains more beautiful.

2 次の英文は,高校生の和樹 (Kazuki) とフィリピン (the Philippines) 出身のベン (Ben) との鉄道 (railway) に関する会話である。 この英文を読んで (1)~(6)の問いに答えなさい。(16点) Kazuki : I hear you like railways. I like railways, too. Ben : Really? Yes! I'm *especially interested in Japanese railways because old Japanese trains are running in the Philippines. Kazuki: Old Japanese trains? A Ben : Yes. Some Japanese people enjoyed watching the old Japanese trains and taking pictures of them in the Philippines. Kazuki: That ( @ ) nice! Ben : Many old Japanese trains are running in some other countries, too. Japanese trains are popular because of their good "quality. Kazuki Our trains are loved "abroad! B Also, I think "reusing things is good. Ben : That's right. Some trains are reused in Japan, too. Kazuki : Oh, really? Ben : Yes. Some of the old trains from the Hibiya Line in Tokyo are now running on the *Hokuriku Rail Road. Kazuki I see. I didn't know that! Ben : One of my good friends likes railways, too. He told me about it ( Kanazawa with him. ) I went to Kazuki: The trains on the Hibiya Line have a *silver *design, right? Ben : Yes, but it "changed. Now it's an orange design. It's the *symbolic color of the Hokuriku Rail Road. Kazuki : Railway lines have their own colors. The symbolic colors of the *Ainokaze Toyama Railway are blue and green. Ben : Blue is the *image of the sea and green is the image of nature like mountains and trees, right? Kazuki: Yes. The designs on the *left and right sides of the train have different colors. Did you know that? Ben : No, I didn't. ( (C) ) are they different? Kazuki : If you look at the side with the blue design, you can see the sea in the *background of the train. If you look at the side with the green design, you can see the mountains in the background of the train. Ben : Wonderful! The design of each side of the train and its background have the same image. I want to take pictures of the trains with the beautiful background.

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英語 高校生

56.58.60.61全然わかりません、、解説お願いします、、😭😭 他も答えあっていますでしょうか🥲🥲

56.Although I have been employed by the company since two years, I have received no increase in my salary of £30,000 a year. During that time the cost of living has risen considerably and I am finding it difficult to make ends meet. 〈上智大 > 57. Our teacher told us that we had to finish the report completely until the day after tomorrow. by 動作や状態が完了する期限 untill 状態の継続 @yntil by 58. 〈広島修道大〉 Although the recent decrease in their income, they decided to continue contributing to the charity foundation which provides financial support for orphans. <東京薬科大〉 ④ 59. The power failure in the entire city lasted for two hours, and electricity finally came back at three o'clock on the afternoon. ③ Coon the afternoon. at = 時刻 〈高崎経済大 〉 60. He went abroad with a view to broaden his mental horizons using the money he had earned doing a part time job. 61. The cost of living can be calculated in ① < 鎌倉女子大 〉 term of the average cost of life's basic necessities, such as food, clothing, and shelter. 3 次の日本文の意味になるように空所に適切な語を入れなさい。 62. 我々のリーダーを信じるかどうかは、あなた次第です。 〈南山大 > It's (up) to you whether you believe our leader or not. up to A A次第で<西南学院大) 63. 期末試験に代えて,レポートを書いてもらおうと思います。 place of A <静岡大) We'd like you to write a term paper in (place) of a final exam. in place of A Aの代わりに

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