多様体の接空間に関する基底定理の証明です。g(q)=∫〜と定義した関数を微積分学の基本定理を用いながら変形してg(q)=g(0)+∑gᵢuⁱと導出するのですが、これがうまくいきません。 自分は、g(q)の式をまず両辺tで微分して、次に両辺uⁱで積分して、最後に両辺tで積分... 続きを読む

12. Theorem.If{ = (x', , x") is a coordinate system in M at p, then its coordinate vectors d, lp, …… 0,l, forma basis for the tangent space T,(M); and D= E(x) 。 i=1 for all ve T(M). Proof. By the preceding remarks we can work solely on the coordinate neighborhood of G. Since u(c) = Othere is no loss of generality in assuming ど(p) = 0eR". Shrinking W if necessary gives E(W) = {qe R":|q| < } for some 8. Ifg is a smooth function on E(W) then for each 1 <isndefine og (tq) dt du g(9) = for all qe {(W). It follows using the fundamental theorem of calculus that g= g(0) + E&,u' on (W). Thus if fe &(M), setting g = f。' yields f= f(P) + Ex on U. Applying d/ax' gives f(p) = (f /0x)(P). Thus applying the tangent vector e to the formula gives (f) = 0+ E(x'(p) + E Ap)u(x) = E(Px). ず ax Since this holds for all f e &(M), the tangent vectors v and Z Ux') d,l, are equal. It remains to show that the coordinate vectors are linearly independent. But if ) a, o.l, = 0, then application to x' yields dxi 0=24 (P) = 2q d」= 4. In particular the (vector space) dimension of T,(M) is the same as the dimension of M.

(5)以外を教えていただきたいです。 名詞構文・無生物主語の単元です。 よろしくお願いします。

1 1[]から適当な語を選び, 必要ならば形を変えて( )に入れなさい。各1回のみ使用可。 A )of the theory of evolution started a new era in history. resign ) surprised all the people in Japan. accepT ) of the project.complete (1) The ( (2) The prime minister's ( (3) There was a big party after the ( (4) I made a (soeak) in Chinese for the first time, and the audience understood me. (5) Agatha Christie is a famous mystery (writer). (6) My mother always takesa (walk) in order to lose weight. [ resign / speak / write / accept / walik / complete ]

英作文の添削をしていただきたいです。よろしくお願いします。見にくいところがあれば言ってください。

Date No. Topic: Da you think that unhedthy fod and drink should be tared at a higher rate than healthy fod? (20- 150vods) agre with the idea that wnheathy food and drink shauld be taxed at a higher rate than healthy food. I have two reasons to support my opineh. Ficst, the number ot peaptle that have an illnes will deerease. Many Jopenese peaple eat wabealitby foad such as fast fed (ロ se patients incease becasse of haring unheaty food. Theretore, it is god for us to decrese oppotuniy of haring the food Second, we can use tax for inventing healthy food. Vnhealthy fod is sold at a lot of super market. a I hink healty fod shadd be insteaded of unhealty fod l0 Heathy food will incre ase by using tar f uaheathy foed lo For these reasens, being tored at_a higher rate is the good iden 13 (12/ mnd) こ Co こ

There is no country in the world *in which all wants can be met, *and this is clearly true at the global level. この文の**の中の文構造がわかりません ここでの... 続きを読む

There is no country in the world *in which all wants can be met, *and this is clearly true at the global level. この文の**の中の文構造がわかりません ここでの... 続きを読む

高校3年生です。分からないので教えてください。！

文法·語量 会話 作文 ● 5 下線部の発音が他の3つと異なるものを選べ。Cirack 03 1. ア. wanted 2. ア.wool 3. ア.farm 1 日本語の意味に合うように( )に適語を入れよ。 イ. stopped ウ、marked エ, washed 詞1.私はその店に走って行ったが,結局閉まっていることが分かっただけだった。 I ran to the store, ( 2.その人は親切にも道を教えてくれた。 The person was kind ( 3.その先生が親切にも私を助けてくれた。 イ. foot ウ, through エ. pull ) find it closed. イ. star ウ) warm エ. garden 4. ア. act イ.salad ウ、 habit , calm エ. southern ) to tell me the way. 5.ア. loud イ. honey ウ. country The teacher was so kind ( to ) help me. 6 次の会話が成立するように( )に適語を入れよ。 ただし,( )内に文字がある場合は 4.私は一言も開き漏らさないように注意深く耳を傾けた。 I listened carefully so ( 5.彼は成長して偉大な科学者になった。 その文字から始まる語を答えること。 Track 04,05, 06,07,08 ) not to miss a single word. 1. A:I'm going to New York next week. He grew up( )a great scientist. B:Iwant( ) call me when you get there. 2. A:Anne, I'd like to (i B:Nice to meet you, Ken. I'm Anne. 3. A:Iwant to learn Chinese. Isn't there anyone who can teach me? ) to my son, Ken. 2」 各組の文がほぼ同じ意味になるように( )に適語を入れよ。 S Do you mind if I open the window? ) Yoko's brother? He speaks Chinese B:(H 1. Do you mind ( *My mother insisted that I should see a doctor. 2. My mother insisted on ( I )(opehing ) the window? very well. )a doctor. 4. A:Do you know that woman? A:The tall one with long hair. 3 各組の文がほぼ同じ意味になるように( )に適語を入れよ。 She spent the whole day just watching television. 1. She did nothing ( 5.A:What country are you from? B:India. A:What's the climate (1 B:It's often very hot in the summer. ) watch television all day. ) in India? Why don't we go to the bookstore? 2. How about( ) to the bookstore? When I hear the song, I always think of my youth. 3. The song always ( 」次の文を英語に直せ。 1.君はそんなに速く歩く必要はない。 (0.5参照) )me of my youth. This bicycle does not belong to me. 4. This bicycle is not ( 2. あなたは将来何になりたいのですか。 (2.7参照) )内の語(旬)を並べかえよ。 4 日本語の文に合うように( 1.先生が私たちにその町の地図を見せてくれた。 (teacher / us / a / our / town / map / of / the / showed). 3. 心配するな。ぐっすり眠ったら気分も良くなるよ。 (ll.7~8参照) 2. エネルギーを浪費するのはいけないと思う。 I(waste / it/ to / energy / think / wrong). 7

なぜ、この答えはBなのでしょうか？ 空所以下の文は不完全な文であると思うのですが、違いますでしょうか？

211. There are certain circumstances may withdraw you from the dontrach] (A) whom (B) where (C) that (D) which ④ 000

まるをつけたwhatever をどう扱うかわかりません

A des 共通関係の把握 39 前置詞が共通語となる共通関係の発見 FA 次の英文の下線部を訳しなさい Only 100 years ago man lived in harmony with nature. There weren't so many people then and their wants were fewer. Whatever wastes were produced could be absorbed by nature and were soon covered over. Today this harmonious relationship is threatened by man's lack of foresight and planning, and by his carelessness and greed. OR-90013 (会) (京都産業大) od この課のテーマも共通関係の発見です。 and に注目しながら例題に取り組み bns 法ましょう。

1から9までを埋めなければならないのですが、質問の意味もよくわからず…。どなたか質問の意味と解き方を教えて頂けると助かります…！

Vocabulary skills: Collocations Read the text. Then find verbs that collocate with the words and phrases below. Write the infinitive of each verb. KEY VOCABULARY SKILLS STUDY SHEET 7, PAGE 164 The Duke of Edinburgh’'s Award The Duke of Edinburgh's Award (known as the DofE) began in the U.K. in 1956. It gives young people from all backgrounds an opportunity to experience challenge and adventure, acquire new skills, and make new friends. Each year, participants between the ages of 14 and 24 complete many hours of voluntary community work. There are three levels: Bronze, Silver, and Gold. Each one requires increasing commitment, so you can choose which level is best for you. There are four sections at Bronze and Silver level, and five at Gold. These sections combine practical, cultural, and adventurous activities. Achieving a Duke of Edinburgh's Award helps young people to develop a sense of responsibility, and promotes values of persistence, commitment, and enterprise. It has a lasting impact on young people's behavior, skils, and life chances. In 1988, the DofE was expanded to become international. These days, over 635,000 participants around the world are achieving a DofE at any one time. Since the DofE began, Over six million young people in over 123 countries have taken part, and it continues to grow in popularity. 1 an appointment / small talk / progress success / your goals / independence dark / older / crops 2 4 a course / a form / an exercise someone a chance / a talk / feedback 5 awareness / growth / competition a qualification / knowledge / a reputation for something a problem / dificulty / something at first hand a friendship / a taste for something / an idea 6 7 8 9 Predicting Look at the title of the information sheet you’re going to read. Discus with a partner what. think you'll read about. Gnbal Youth Service Day

模試の問題の解説なんですけど、❔の関係詞のところがいまいちわからないです。その後の文の We had reading the mapってどこが抜けてるんですか？関係詞を使うときは主語とか目的語が抜けててその説明をするってイメージだったのですが、主語も目的語もあるのになんでw... 続きを読む

(5) 正解は,アーエーカーイーウーオ。 完成文 Despite the difficulty we had reading the map, we managed to get there on time. (訳例 地図を読むのに苦労したにもかかわらず,我々は何とか時間通りにそこにたど り着くことができた。 ○まずは語群に与えられた had, reading. the difficulty に注目し、S have difficulty - ing 「S は-するのに苦労する」という熟語を軸にした we had the difficulty reading the map と いう骨格を想定してみる。 ○ただし, 語群に残った despite 「…にもかかわらず」は前置詞であり, 文を続けること はできないので, despite we had the difficulty reading the い(ちなみに、despite の代わりに接続詞 though [although] を用いて though [although] we had the difficulty reading the map とまとめれば正しい英語となる)。 we had the difficulty reading the map から the difficulty を切り離し,前置詞 despite の 直後に移動して despite the difficulty とまとめ, 残った we had reading the map を関係 詞節として the difficulty の直後に添えれば,despite the difficulty (that [which]) we had reading the map (我々が地図を読むのに経験した苦労にもかかわらず→我々は地図を 読むのに苦労したにもかかわらず)となり, 文法的にも内容的にも適切に後半部分とつ map とまとめることはできな ながる。