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数学 大学生・専門学校生・社会人

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.

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TOEIC・英語 大学生・専門学校生・社会人

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

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英語 高校生

添削お願いします🙇‍♀️

下記の英文を読んで設問に答えなさい。*の付いている語句に関しては本文の後にまとめて注 があります。 Jason paced the corridor* outside the boardroom* before his presentation. He could heat his pulse (イ) his ears, and his mouth was dry. (1)The last time he felt like this. he told himself to relax. but it didn't work. So this time, he tried something different: "I feel excited." Suddenly, his symptoms* the racing pulse, the twisting stomach, the sweaty palms-started to energize him. The boardroom door opened. He performed brilliantly. This story might be fiction, butat its core lies a very real truth. (2)The science of emotion tells us that our bodies respond( similarly to many different emotions, including anger, excitement and anxiety, And recent research has, shown that if we verbally* put those symptoms into a different context-by saying "I feel excited" when feeling stressed, for example-we can trick ourselves into following suit*. The key to all this is the neurotransmitter*| and hormone norepinephrine*. When you're too stressed or scared, your norepinephrine levels surge* well(ロ)their sweet spot*;/when you tell yourself you're excited,they sometimes fall back. Of course, (3)this trick won't work (ハ) every emotion: it's a lot harder to reframe stress )(ニ) relaxation, because those two conditions have entirely different physical symptoms. Nonetheless, in the right context, stress can become a source of positive energy-not just a by-product* of anxiety. (出典)Ian Robertson, “How Stressing Out Can Help You Succeed", Time, 189 巻,4号,p.15, Jan. 23, 2017. (注) corridor:廊下 boardroom:重役会議室 symptom:症状 verbally: 言葉で neurotransmitter : 神経伝達物質 フリン(興奮を伝達する脳内ホルモンの一種で、ノルアドレナリンとも呼ぶ) surge: 急上昇する、 わき立つ sweet spot : 最適なレベル follow suit:それに従う hormone norepinephrine : ホルモン·ノルエピネ by-product:副産物 彼生が最後にこのように感じたとき、彼失はソラックスするように [設問1] [設問2] 【設問3) [設問4] 下線部(1)を和訳しなさい。 自分に言い開かセたが、 それはりまくいがながった。 下線部(2)を和訳しなさい。 下線部(3)this trickの事例を本文に即して具体的に日本語で説明しなさい。 文中の空欄(イ)~ (=) に入る最も適切な語をそれぞれ次の1から6の中か ら選び番号で答えなさい。 1. after )2(ロ)6. (1)4()ゲ 6. beyond 2. for 3. as 4. * to 5. in (2)情の科学は和たちの体がが怒りや興香,不要すなど、多くの果なる感情に対して、 同じょうに反応することを私たらに伝えている。. (3)身に楽しいいと感じるウに言間けせなと、 1レアドレオリンの分泌量が減ることにより、 ストレスが軽非するということ。

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