多様体の接ベクトルに関する性質の証明なんですけど、(1)が分かりません。 素直に訳すと、(1)は「多様体上の滑らかな関数fとgが点pの座標近傍で同じなら、その接ベクトルv(f)とv(g)は同じになる」だと思うんですけど、証明でf(p)=0,g(p)=1と明らかに異なる値をと... 続きを読む

11. Lemma. Let ve T,(M). (1) If f, ge F(M) are equal on a neighbor- hood of p, then Uf) = v(g). (2) If he F(M) is constant on a neighborhood of p, then u(h) 0. 三 Proof.(1) By linearity it suffices to show that if f = 0 on a neighbor- hood W of p, then u(f) = 0. Let g be a bump function at p with support in W; then fg = 0onall of M. But v(0)= u(0 + 0) = u(0) + u(0) implies v(0) = 0. Thus 0= (fg) = v(S)g(p) + f(p)v{g) = u(f), since f(p) (2) By(1) we can assume that h has constant value c on all of M. If 1 is the constant function of value 1, then 0 and g(p) 1. ニ (1) = (1.1) = (1)1 + lu(1) = 2v(1). Hence v(1) = 0, and v(h) = u(c· 1) = cu{1) = 0.

問題の解き方や、答えが分からないです。また、問題を解くために高校数学や大学数学のどの単元の知識が使われているのかも合わせて教えて頂きたいです。よろしくお願いします。

問(i)~(vi) に答えよ。 解答は解答用紙の所定欄に日本語で記すこと。 導出過程も簡潔に記す こと。 Let the function f(n) be defined as S(n) = cos? where n and 入 are positive integers (greater than 0). (i) Assuming n>1000 and 42 < 76, determine f(n). (i) Assuming is a prime number, determine the smallest n such that 『(n) = cos? %D

左の写真を見て右の問題を解かないといけないんですけど、どなたか教えてほしいです 多いですけどよろしくお願いします🙇‍♀️

*健の住む山川町で,国際交流プログラム(International Exchange Program) が開催されます。次は, ip.4~32 プログラムのパンフレットの一部です。 これを読んで, あとの問いに答えなさい。 Yamakawa-cho International Exchange Program Date August 20 Place Yamakawa Arena* Part*1(9:00 A.M. ~ 10:00 A.M.) Self-Introduction Meeting* First, please make groups and talk about the things below* : * What's your name? like? * Where are you from? After that, we are going to play some games. * What do you Part 2(10:00 A.M. ~ 2:00 P.M.) Experience One of Three Courses* ※Please choose one course when you apply for* the program. Course A Course B Course C Go to Yamakawa Museum Enjoy Shamisen Music Hiking at Aoi Park We are qoing to learn*|The shamisen is a traditional | We are going to go to Aoi about the history of this instrument* in this town. Park by bus. You can enjoy A famous shamisen player, beautiful natural* things there. You can see ukiyoe of| Goto Ryuji, will play at| The birds and flowers are town there. Utagawa Hiroshige. You can try on* yoroi and| After that, you can try the | When you see them, please Yamakawa Hall. popular. katana. shamisen. take pictures. ※In each course, the staff* will prepare lunch boxes for you. Part 3 (2:00 P.M. ~4:00 P.M.) Make English Posters We are going to make groups again. Talk about your experiences* to each other and make posters of the museum, the shamisen, or the park in English. (注) arena アリーナ Part 第…部 Self-Introduction Meeting 自己紹介の会 below 下の コース apply for …に応募する COurse learn 学ぶ try on …を着てみる instrument 楽器 natural 自然の staff スタッフ experience 体験

コミュ英です 解ける方いましたらお願いします 提出が迫っている科目がいっぱいありすぎて、手が足りないので助けていただけると助かります…

1.次の英文に主部と述部の境界線を例のように入れなさい。 そのあと全文を日本 語に訳しなさい。 dT (1 T (S M (8 例:European countries / can be divided into three groups. ① The watch stolen from the shop was a valuable one. ②) The bookI wanted was written by Natsume Soseki. wIO ③ The girl with long hair gave the police some information. 0 b of 4 The missing girl wandering about the woods was found dead. 5 The news of the accident makes me sad. 6 The telephone on the desk rang loudly. の Takeshi, my brother, used a knife to open the letter. 8 Mastering a foreign language takes longer than learning to ride a bicycle. bag 設問2.次の英語の下線部の品詞名を書きなさい。また英文を日本語に訳しなさい。 1) My father is younger than he looks.(183mの意 2) He worked hard to provide for his old age. 3)I have often been to India. 4)I always use a dictionary for the use of students. 5)I remember the man very clearly. 開 190 noidom adT ((I Nbollid uor ) () lusittib 19ukngt6 9d g, olig .019) 0slqis ) () 6) Stationary cars in traffic jams cause a great deal of pollution. kti2z0q 設問3.次の文の主語S、 動詞V、目的語O、補語C、付加語Aなどに下線を引き分析 をしてから、全文を日本語に訳しなさい。 例:I like dogs and cats. 私は犬と猫が好きです。 SV diw baans bns zad 1) His mother handed him a bag. 2) My sister taught me Japanese history. ob Juods gnidaidt al sde 2aniand 3) 16 149 n 9ob buedaud Tod 2ai2 (8 He had a chance to meet his father. 4) You have made me what I am today. 入る 設問4.次の日本語を指定された文型を用いて英語に訳しなさい。 1)私たちは父の誕生日を祝うためにパーティをした。SVOA 2)父は私に新しい靴を買ってくれた。 SVOO 3)私は危険に気づいていた。 SVCA hnイー

どうしてcountriesになるんですか？どの選択肢も絶対違うなって決めれなかったのでできれば4つともどうして違うか教えてください

English is (speaks, spoke, spoken, speaking) in many(countries, people, group, e(近畿大附 ·改) Spoken mntKASS lands) of the world. A new camera was(màde, listened, bought, given) to me on my birthday.

画像の問題で、1〜4の中で文法的に間違っているものを選んで正しく直すという問題です。答えは3を「should be recalled」にするということだったのですが、「urged」と過去形があるので、時制の関係で「should have been recalled」になるの... 続きを読む

Te Bill tl using yo Yes, The consumer, group (1)urged.that (2)all the defective tires (3)should recall (4)immediately. yq nor srce (法政大) boar 8 98u 98 binos . By this time next vear. our new office will ( )in Canado

The gold rush that followed attracted many prospectors の構文教えて頂きたいです🙇‍♀️

world/ for forty thousand years.. The veil would_not be lifted Aintil gold was e discovered in a *tributary/ of one of the main rivers."The gold rush that followed attracted many prospectors, including Michael Leahy, an Australian who on May 26, 1930) set out to look for gold/in the mountains/with a fellow prospector/ anda group of native lowland people hired as carriers

なんで1800円抜いてるのでしょうか？

B You visited your high school website and found information about_a walking tour in Kyoto. High School Website The English club is hosting a walking tour in Kyoto for the students and teachers who are visiting from our sister school in Sydney, Australia. We 5 are inviting the students of this school to join us, and any parents who want to volunteer to be guides are welcome, too. We have rented drop us off close to Kinkakuji and pick us up close to Ninnaji Temple. bus that will The leaves are beginning to turn color, so Kyoto will be especially beautiful. But it may also be very crowded with tourists. Hopefully, there will be fewer people at the second and third World Heritage Sites. 10 Walking Tour Schedule 7:30 a.m. The bus leaves from the school parking lot. 9:00 a.m. Enter the grounds of Kinkakuji. へ00 00 (World Heritage Site, Admission: 400 yen) 15 11:00 a.m. Enter the grounds of Ryoanji Temple as a group. (World Heritage Site, Admission 500 yeny 200 12:30 p.m. Eat lunch at Shojin Ryori Restaurant. (The standard course meal: /1,800 yen) 2:00 p.m. Enter the grounds of Ninnaji Temple as a group. (World Heritage Site, Admission: 500 yeny 20 3:30 p.m. The chartered bus will take everyone back to the school parking lot. ●Students may choose not to ride buses between the temples, especially if the weather is good, but the adults should keep in mind that it takes about an hour to walk around each place, we will be visiting/ It might be 25 a good idea for them to spend some time relaxing at cafés or tea shops and then ride buses instead of walking. To register to join the tour, click here. To join the lunch at Shojin Ryori Restaurant, click here. 1-6

一番目が問題で二問目が答えなんでがわかる方教えください

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x→f(x). The ordered pair (x, S(x)) belongs to the function f. Ifxisa real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), S(a), and f(6+a) for f(x) 三 3° X - b) Find g(7), g(h), and g(7+h) for g(x) = 16+ 3x x. 2 Find k(9), 4k(a), and k(4a) for k(x) Vx c) 2 For the above functions, determine the resulting domain. Solutions: a) b) c)

一番目が問題で二問目が答えなんでがわかる方教えください

EVALUATING FUNCTIONS The symbol f(x) represents the real number in the range of the function f corresponding to the domain value x. Symbolically, f:x→f(x). The ordered pair (x, S(x)) belongs to the function f. Ifxisa real number that is not in the domain of f, then fis not defined at x and f(x) does not exist. Examples: 15 a) Find f(6), S(a), and f(6+a) for f(x) 三 3° X - b) Find g(7), g(h), and g(7+h) for g(x) = 16+ 3x x. 2 Find k(9), 4k(a), and k(4a) for k(x) Vx c) 2 For the above functions, determine the resulting domain. Solutions: a) b) c)