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Mathematics Senior High

(3)の部分分数分解の仕方に納得いきません なぜXとX^2とX -1に分けられるのでしょうか?

頻出 ★☆☆ 例題 142分数関数の不定積分 次の不定積分を求めよ。 (1) 12x²-x-2 dx (2) (2) S dx (1)~(3) いずれも f'(x) f(x) 次数を下げる の形ではない。 (x+1)(2x+1) dx 頻 (3)√x²(x-1) 次数下げが、 わからん (1) Re Action (分子の次数)≧(分母の次数)の分数式は、 除法で分子の次数を下げよ B 例題 17 (2), (3) 分母が積の形部分分数分解 1 a b x+1 2x+1 (2) (x+1) (2x+1) 1 (3) x²(x-1) ax+6 x2 C +. a b x-1 + + x 17 x² x-1 Action» 分数関数の積分は,分子の次数を下げ、部分分数分解せよ 2x²-x-2 dx = √(2x-3+x+1)dx (1) S2 x+1 1 -1)、 61 (x+1)(2x+1) はらうと より 52x =x 2-3.x +log|x+1+C a + a, b, c の値を求める 4 分子を分母で割ると 2x-3, 余り 1 不定積分 b とおいて, 分母を部分分数分解 x+1 2x+1 a(2x+1)+6(x+1)=1 (2a+b)x+α+6-1 = 0 係数を比較すると, α = -1,6=2より (x J+1+ dx +1)(x+1)=(x+ 2 dx 2x+1 = -log|x +1 + log|2x + 1 + C (2a+b)x+α+6-1 = 0 はxについての恒等式で あるから 2a+b=0 la+6-1=0 )より sin 20 2 -dx 2x+1' = =10g | 2x+1 +C x+1 | = 2.1/23log|2x +1|+C 2 1 a b C 61 (3) + + x-1 うと x²(x-1) x ax(x-1)+6(x-1)+ cx2 = 1 (a+c)x2+(-a+b)x-6-1 = 0 係数を比較すると,α = -1,b=-1,c=1 より xについての恒等式であ るから fa+c=0 とおいて、分母をはら 部分分数の分け方 意する。 dx 1 1 1 + x2 x-1 1 問題141 -log|x| + 1 +log| JC ■142 次の不定積分を求めよ。 (1) √ x2+3x-2 x-1 dx x +log|x -1|+C x- +C JC (2) St 3x+4 d -dx (x+1)(x+2) -a+b=0 l-b-1=0 dx (3) √x(x + 1)² p.281 問題 142 269

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TOEIC・English Undergraduate

この長文問題の答えと解説をお願いします。

15 語数: 398 語 出題校 法政大 5 We are already aware that our every move online is tracked and analyzed. But you 2-53 couldn't have known how much Facebook can learn about you from the smallest of social interactions - a 'like'*. (1) Researchers from the University of Cambridge designed (2) a simple machine-learning 2-54 system to predict Facebook users' personal information based solely on which pages they had liked. E "We were completely surprised by the accuracy of the predictions," says Michael 2-55 Kosinski, lead researcher of the project. Kosinski and colleagues built the system by scanning likes for a sample of 58,000 volunteers, and matching them up with other 10 profile details such as age, gender, and relationship status. They also matched up those likes with the results of personality and intelligence tests the volunteers had taken. The team then used their model to make predictions about other volunteers, based solely on their likes. The system can distinguish between the profiles of black and white Facebook users, 15 getting it right 95 percent of the time. It was also 90 percent accurate in separating males and females, Democrats and Republicans. Personality traits like openness and intelligence were also estimated based on likes, and were as accurate in some areas as a standard personality test designed for the task. Mixing what a user likes with many kinds of other data from their real-life activities could improve these predictions even more. 20 Voting records, utility bills and marriage records are already being added to Facebook's database, where they are easier to analyze. Facebook recently partnered with offline data companies, which all collect this kind of information. This move will allow even deeper insights into the behavior of the web users. 25 30 (3) - Sarah Downey, a lawyer and analyst with a privacy technology company, foresees insurers using the information gained by Facebook to help them identify risky customers, and perhaps charge them with higher fees. But there are potential benefits for users, too. Kosinski suggests that Facebook could end up as an online locker for your personal information, releasing your profiles at your command to help you with career planning. Downey says the research is the first solid example of the kinds of insights that can be made through Facebook. "This study is a great example of how the little things you do online show so much about you,” she says. "You might not remember liking things, " but Facebook remembers and (4) it all adds up.", * a 'like': フェイスブック上で個人の好みを表示する機能。 日本語版のフェイスブックでは「いいね!」 と表記される。 2-56 2-57 2-58 36

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English Senior High

英語のこの問題の解答をおしえてほしいです。おねがいします!

・あなたは、外国人の知り合い (Jake) から、Eメールで質問を受け取りました。 この質問にわかりやすく答え る返信メールを、【 】に英文で書きなさい。 ・あなたが書く返信メールの中で、 Jake のEメール文中の下線部について,あなたがより理解を深めるため 下線部の特徴を問う具体的な質問を2つしなさい。 ・あなたが書く返信メールの中で【 】に書く英文の語数の目安は 40語~50語です。 解答は、解答用紙の裏面にあるEメール解答欄に書きなさい。なお、解答様の外に書かれたものは採点され ません。 ・解答が Jake のEメールに対応していないと判断された場合は、0点と採点されることがあります。Jake の E メールの内容をよく読んでから答えてください。 Hi! 】 の下の Best wishes, の後にあなたの名前を書く必要はありません。 Guess what! My parents gave me a camera for my birthday last week. I was very happy because I'd never ow ned a camera before. I take photos with it every day. I'll take a picture of you the next time I see you. Taking photos is great fun, but my camera has too many functions. I don't know how to use them all. Do you think cameras will become more popular in the future? Your friend, Jake Hi, Jake! Thank you Best wishes, for your e-mail.

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