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TOEIC・英語 大学生・専門学校生・社会人

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Questions 5-7 refer to the following letter. a new member to the club To welcome confirm To | continued membership Mr. Leonardo Harper 571-45 Heiligenstàdter Street Vienna 1190 の) December 15 Dear Mr. Harper, Thank you for your continued support of the North Vienna Concert Hall We are writing to confirm receipt on December 14 of your North Vienna Club membership renewal payment for next year. Alnterviews with musicians To celebrate our 30 year anniversary, we are happy to announce some new special benefits for club members. Starting next year, club members can receive a 10% discount on any concert held during the first three months of the year. Call our ticket office at 1-5123098 and use the promotional code CZ1713 when you order your tickets. Please note that discounts only apply to pre-orders placed during this special period. IC) Commentaries on 0 The concert schedule performances As always, members will receive our monthly magazine, North Vienna Club, which features concert reviews and interviews with various artists and musicians, together with news and schedules of all of the events at the concert hall. Next month's issue will feature a six-page interview with the world famous conductor Franz Minsky. Once again, we thank you for being a North Vienna Club member and for supporting arts and music in our community. Sincerely, Roy Pophins Roy Hopkins Director North Vienna Concert Hall の の)

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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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