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English Junior High

日本語の意味が分かりません💦 教えて下さると助かります! すみませんがお願いします!

【ゆりさんのスピーチ】 Do you know that a lot of people in Shiga Prefecture have worked as volunteers? I read about it in the newspaper and I thought of one person, Mr. Ikeda. I think most of you know him. He lives near here and he takes care of the flowers along the road to our school. One day, I said to him, “Thank you very much for taking care of the flowers. beautiful.” He smiled and said to me, “It's my pleasure. I'm glad that you I like seeing them. They're very enjoy O them. It's only a small thing, but I wanted to do it for the people in our town.” I wanted to do something for other people like Mr. Ikeda. So I decided to clean the lakeshore whenI take a walk every morning. When I walk along the lakeshore, I always enjoy the beautiful view. I ② (enjoy / to / wanted / everyone ) the beautiful view of Lake Biwa like me. While I am picking up garbage on the lakeshore, many people say to me, “Thank you.” When I hear that, I am very happy. After strong winds, the lakeshore gets very dirty. Cleaning it is hard, but I don't feel tired because 3) When I was a child, I only did things that other people asked me to do. Through this experience, I've learned that it's important to decide what to do for others by myself. Aweek ago, I had another wonderful experience. When I was cleaning the lakeshore, I met a woman who was doing the same thing. She said to me, Thank you for keeping the lakeshore clean. I see you when I take a walk every morning. I was moved, so I began to clean like you.” I was glad to hear that. I found that even a small thing can move people if we do it for others. I also learned that volunteer work will spread to other people in this way. I hope everyone will do something for other people like Mr. Ikeda. (注)It's my pleasure. どういたしまして。 lakeshore 湖岸 view 眺め garbage ごみ dirty よごれた by myself 自分で move (d) move(感動させる)の過去分詞形

Resolved Answers: 1
Mathematics Undergraduate

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... Read More

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.

Unresolved Answers: 1
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