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Mathematics Undergraduate

写真2枚目のtのn乗の係数を求める時になんで2xというのが出てくるのかがわからないので教えてください。その上に書いているtの4乗の時の例も何を言っているのかがわかりません。教えてください！

(ローアー2xア。 0 隅較2 の り (1のP。ブー2rP。+a(gキりう ー の xア。 _papのうすtm(m りー (at1))Pp。 0 これを変形して, (< と (P。P。ーアPP) ー2(P。アメーカー =人a(なりーが(TjP。p。 T 衣86のニア。P。) ) 胡 (G-の(PP) ( (1ー9(P-P。ーPaP。うニー2r(P。 アーアー 1 fa(e+1)-m(m+1)Pep。=英(Q の)(P。アP,ーP。P/))} この両辺を積分区間[-1, 11で*により積分すると (eat1) (m+1) / P。Pzな=[Gーェ(Peアー 「.29】 ょって, この両辺を ヵ(ヵ1) 一刀(十1) (キ0) で割ると、 間交條の式: / 『P。(*)P。(<) =0 が導けるんだね。 1 次 maのとき,/ZaG)) ニテ をしたいんだけれと このためにはまず, 次のルジャンドル多項式の “母関数"(gezcrorip 7zzcffoz) の公式 : 隊計968 ーー…(*7) を示さなければならない
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TOEIC・English Undergraduate

穴埋めを教えて欲しいです！！

are the sentences below using words from the box ん compietion- Compi track zone random schedule ar massive holes into the ground near 。 Scientists rhguake faulr areas to learm what is happening nder the surface edictis that they dont they One resson erthquakes are so hard to Pr cem to follow any regular Pattern Or appear to occur almost at ーー _ he movements of the Earths 3. Scientists who __ 三 _ earthquake, known as "the rust believe that a___ eventually occur in southern California Big One・ wl 4 Research aNer the 2004 Asian tsunami found only two dead pufaloes in a large wildlife conserVation sri Lanka. This led to renewed belief that animals are sensitVe tの the near arrival of earthquakes B. Completion、Complete the information with words from the box. い One word is extra ^ ーー ーーーー ーーーーーーーーーー ーー コ emeo | aak。 detect laboratory 。 precise schedule | 9 に 還 "。。 ーー ーー ーー Pe Ost Researchers collecting 1 from experiments in a amd 2. , as well as those observing animals in the real ae bee world, suggest that animals are much more aware of the world around them than we human beings. For example, some scientists believe that dogs can be used to predict earthquakes. Mitsuaki Ota of Azabu big Universiby, Japan, dlaims that dogs can 3. earthquakes about three hours before they happen. SOme scientists are confident that with the help of dogs, one day more を predictions could be possible.
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TOEIC・English Undergraduate

空きに入る単語を教えてくださいm(_ _)m

本ee 半 nces below using words from the box sssdomi iscbeun "5 dr holes into the ground near 1 iearm what is happening under the surface 1 Scientsts ーー carthquake fault area aarthquakes are so hard to predict is that they dont ー:tey 2. Onereaso aem to follow any regUlar Ds appearto occur almost at 一 ane1OthOEだおーーー DO of the Earths DGGSthSDaS euAO IO3 Big One" wil eventualy occur in southerm Caliormia atuern 0cにニーニー Research aRer the 2004 Asian tsunami found only two dead im puffaloes in alarge wildHife conservation sri Lanka. This led to renewed belief that animals are SenSiHVe to te near arrival of earthquakes. Complete the information with words from the box. Completion. One word is extra, へ A是 ー___ 一一 ーーーーーーー empo | ake 。 detect laboratory 。 precise schedule 1995 ーー 一一 jm oet Researchers collecting 1 from experiments in a add 2 . as well as those observing animals in the real de Mg word, suggest that animals are much more aware of the world around them than we human beings. For example, some scientists believe iiat dogs can be used to predict earthquakes. Mitsuaki Ota of Azabu Universiby, Japan, daims that dogs can 3. big earthquakes about three hours before they happen. Some sientsts are confident that with the help of dogs, one day more 4_ predidlionscouldbepossible.
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Mathematics Undergraduate

解説お願いします。

リピ 間題はとう 5 グラフの形はしっかり頭に入っただろうか. COA (凍画4 次のグラフを措け。4=41 で4 ( も 1 この式がどんな意味をるっているかを理解すればわかり すくなる. 評しい説明は薬学の専門科目の先生に聞くと よい. イー り選応がカ次訂式4 = 4eのに従うとき。 反応物4と 成物のの感には次の式が成り立つ. イ+グ= タールー-4=4ー4eY=40-eの ンクは中しならんにかる。ナなわち、生過生9のクララフ は4から友応物4 をいたグラ フが靖ければよい 例26).
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