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Mathematics Senior High

極限の問題です 黄色マーカーで引いたところの解説をお願いします

基礎問 90 第4章 極 51 数列・関数の極限(L)(b)別リアル) X X X X X ? L ① (2) BR る. (1) 一般項am をnで表せ. 数列 {an} は, a1= =1/12/1 .. (2) Sm= Can をnで表せ. k=1 精講 (n+2)an+1=nan (n=1,2, ・・・) をみたしてい (3) lim (S)" を求めよ.ただし, lim 11-00 典型的な極限の問題です. (1) は数学Bの範囲ですが, 漸化式のなかでは, 難しいほうに入りま す。(数学ⅡI・Bの基礎問では扱っていません) そこで,次のパターンを覚えておくことになります。 (an+1=f(n) an (f(n): 分数式) 型漸化式の解き方〉 2 (1+1 ) ² = e ak+1 ak (3)のただしがきにある 「lim (1+1/2)"= →∞ 72-00 -= =f(k) として,kに1,2,.., n-1 を代入して辺々かける。ただし =e」 は受験生が正しく使えない公式の 代表格ですが,大切な公式です。 使い方にコツがあるので, ポイントをよくみ てください 解答 (1) (n+2)an+1=nan より ak+1 k ak k+2 A₂ A³ a₁ az 1,2,.... n-1 を代入して, 辺々かけると n≧2のとき, 「い冷合わせるため を用いてよい。 an 1.23 an-1 3 4 5 n−2_n_l n n+1 an 2 = よって, as n(n+1) F-t, a== n(n+1) (a₁ = 1/29) これは,n=1のときも含むので, かけ終わりかけ 初めより, n-121 これから n≧2 辺々かける an n(n+1) (別解)(かなり速いのですが、理解しにくいかもしれません) (+2)an+1=nan の両辺に n +1 をかけると, (+2)(n+1)an+1=(n+1)nan ゆえに, 数列{(n+1) nan) は, 初項 2.1.a=1, 公比1の等比数列. よって, n(n+1)an=1 iha (2) (数学ⅡIB119) Sn= = ²₁R (k² + 1) = ² ( 1/² - x + 1) = 1 (3) (S.)-(1)-("+¹)*((₁+²) = tim (S.)*=lim{(1+2)^- 11-00 ポイント 演習問題 51 .. an= 1 (別解) (S)"=(1- 1) において,(n+1)=N とおくと, -N-1 △→∞ (S.)-(1+) -(1+)*(1 + 2 ) " - ((₁ + + ) * T * (₁ + 2 ) " N n→∞ のとき, N- ∞ だから, lim (S.)" =— Jim_{(1 + + )"}*(¹ + ) ¹ = 0 ²¹ = 1/ n→∞ e + (1) lim 1 n(n+1) =e (△はすべて同じもの) 次の極限値を求めよ. 2n no 2n+1) 1 n n+1 n+1 ² = = e = ¹ = ² ( (数学ⅡI・B64 指数の計算) 1 注 この公式は「△→±∞」で成りたちます. 0 91 (2) lim (1+- 71-00 2n 第4章

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Physics Senior High

物理の電気の問題です。 黄色マーカーで引いたところの解説お願いします

合成抵抗 **120 【8分・12点】 合成抵抗 0 0 黒鉛筆で方眼紙のマスを濃く均一に塗りつぶして電気抵抗を作り, 合成抵抗の実験 をする。図1のように,2×1マスの太線を2本描き,太線の端を導線に接続し、 線の他端を端子に接続する。端子間の合成抵抗をテスターを使って測定する。ただ し,同じ幅の太線の抵抗は長さに比例するものとし, 方眼紙は電気を通さないものと する。 電気と磁気 2 2 ① 端子 図1 問1 図2のように, 12×1マスの太線を描き加え,太線の端を導線で端子に接続す る。この操作を繰り返して行い, 1回ごとに合成抵抗を測定する。 太線の数Mに 対する合成抵抗の測定値を示した図として最も適当なものを一つ選べ。 ・・・・・・・・・・ 黒鉛筆で塗りつぶした太線 M=3 4 6 太線の数 M 基 XXXXXXX 4 6 太線の数M 方眼紙 合成抵抗 合成抵抗 図2 0 2 4 6 0 端子 太線の数 M 2 4 6 テスター 太線の数 M to CHEESEN COMERCICICIBERCO MAR MARCAS DE DESERONO M=6 合成抵抗 0 2 4 6 太線の数M 問2 図3のように,太線を6等分した位置に針金の両端を接続し、 針金の数を増や しながら, そのつど合成抵抗を測定する。 最初の針金は太線の左端から2マス離れ た位置に置き, 2マス間隔で順次針金を追加する。 針金の数NZ対する合成抵抗 の測定値を示した図として最も適当なものを一つ選べ。 ただし, 針金の抵抗と太さ は無視できるものとする。 合成抵抗 合成抵抗 針金 トートート ① 2012345 針金の数N 4 N=1 ① 0.50 012345 合成抵抗 ②1.0 合成抵抗 図3 012345 ② ③ 1.5 針金の数N ⑤ 012345 §4 電流 155 導線: 図 4 ④ 3.0 BE WA BA 針金の数N 針金の数N 間3 図4のように,太線を3等分した二つの位置に抵抗と太さが無視できる針金の 両端を接続し,さらに, 2本の針金を導線で接続する。 12×1マスの太線1本の抵 抗を3.0kΩとすると, 合成抵抗の値はいくらか。 ただし, 導線の抵抗は無視でき るものとする。 kΩ de 48 48 N=5 合成抵抗 012345 針金の数N ⑤ 6.0

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English Senior High

日本語訳をお願いしたいです!!お願いします

次の英文を読んで、設問に答えなさい。 Everybody wants to eat delicious and safe food. However, exposure to different cultures reveals 2 how people's attitudes towards food safety and taste are not all innate or biological. Assumptions and practices regarding the preparation and presentation of food highlight the influence of culture on what and how people eat. For example, in one culture, some kinds of fresh ingredients might be considered edible (a), that is, without any kind of preparation like washing, peeling or heating. Yet in another culture, the same foodstuff may require some kind of preparation before it can be eaten. It is often difficult for people from the same culture to view such activities and beliefs objectively, and so witnessing the food practices of other cultures can be surprising. Sashimi is a great example of this. While sashimi may be the result of several steps of preparation from cleaning and cutting, to a particular style of presentation - heating is not one of these steps. (2)Japanese consumers take it for granted Cultures, the conventional belief may be that real and fish require some sort of cooking, such as baking or frying, (3) in order (b) them to be considered edible. In these cultures, sashimi is not thought of as raw, delicious and safe to eat, but rather as uncooked, and therefore possibly unsafe to eat, regardless of how it may taste. Fresh chicken eggs are another raw foodstuff commonly eaten in Japan — as a topping for rice, or as a dipping sauce for sukiyaki, for example but most people in the UK or the USA believe that chicken eggs require some kind of heating before they are fit for human consumption. However, the ways in which people from other cultural backgrounds eat certain foods might be considered equally unconventional by many Japanese. For example, few Japanese would eat the skin of apples or grapes. In this case, the difference involved in the preparation of the food is not the use of heat, but the removal of part of the foodstuff. People in much of the world eat apples and grapes without peeling them. A European might think, What could be more healthy and delicious than picking an apple from the tree and eating it?' But this way of thinking is not shared by a large number of Japanese. (4) It is clear that different cultures have different conventions regarding the preparation of particular foods, and different beliefs about what is considered delicious. However, there is no question that some common food preparation practices - or sometimes a lack of certain food preparation processes - are unsafe from a scientific point of view. However delicious they may be, raw meat and fish can contain the eggs of harmful parasites like tapeworms, which are often undetectable. If chicken eggs are not properly stored, and are left unconsumed for a long time, they can easily produce bacteria like salmonella. The poisoning caused by salmonella does not usually require hospitalization, but it can be very dangerous for young children and elderly people. In addition, while eating the skin of apples and grapes may be a good source of dietary fiber, one also runs the risk of consuming insecticides, the poisons that are used to protect many non-organically farmed fruits from insects. So, while there may be 'no accounting for taste' beyond culture, safety is a different issue, and (5) we should always be aware of the risks involved with culturally accepted methods of food production and consumption. 問1 下線部 (1)で,空欄 ( a )に入る最も適切な語句を, (A)~(D)から選び, 記号で答えなさい。 (A) as is clear (B) as is fresh (C) as they are (D) as unclean 問2 問3 問4 問5 下線部(2)を日本語に訳しなさい。 下線部 (3)の空欄(b)に入る語(1語) を書きなさい。 下線部(4) を日本語に訳しなさい。 下線部 (5)の理由として最も適切なものを, (A)~(D) から選び,記号で答えなさい。 (A) Eating raw chicken eggs or unpeeled fruits can be dangerous in certain conditions because of harmful bacteria or pesticides. (B) Eating unpeeled apples or grapes may cause weight gain. (C) Only young children and elderly people are vulnerable to particular bacteria. (D) Beliefs about what is considered delicious actually come from better understanding of food preparation. 問6 本文の内容と一致するものを, (A)~(G)から3つ選び,記号で答えなさい。 (A) By food preparation processes, the author exclusively means the use of heat. (B) Culturally established ways of consuming food may conflict with scientific principles of food safety. (C) In some food cultures outside Japan, fish in its raw state is not categorized as an edible foodstuff. (D) People having little contact with other cultures tend to view their own food-related conventions as natural and standard. (E) Repeated exercise is required for the mastery of any food preparation. (F) Instinct alone determines what and how people eat. (G) All cultures around the world consider it natural to eat unpeeled fruit.

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