学年

質問の種類

英語 高校生

このso thatはどんな意味ですか?

Growing up as a young boy in Scotland, Alexander Graham Bell showed a unique talent for music. Though he ( 4 ) this path through to a career, Bell changed his mind and followed in his father's footsteps. His father wás a famous teacher of speech communication. Bell becanme a teacher himself, first of music, then of speech communication. At the same time, Bell pursyed his other love, inventing, by-experimenting with the mechanics of Speeth using both Triends and his dog as súbjects. In 1870, when he was 23 years old, Bel and his family sailed from Scotland to Canada to escape the tuberculosis epidemic* that had already killed Bell's two brothers. While his parents remained in Canada, Bell moved to the ている 2ん0 United States to teach. He continued to experiment with his jnterest, electricity. He dreamed of being able to transmit speech, so that people' around the world could ですた。 てる 5 )the spoken word. Bell and his assistant, Tom Watson, achieved their first success in 1875. After many アシスタント Tu 11 成ェや 1に experiments, they were able to invent the telephone. On March 7, 1876, Bell and Watson succeeded in( 6 )inseparate rooms across a small わけ hallway. Later that year, Bell made the first Iong-distance telephone call, overa distance of 16 ゴーク ilometers, to his father while on vacation in Canada. Thanks to his invention, we can nov communicate and share information with people all over the world.

解決済み 回答数: 1
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.

未解決 回答数: 1