答えと解説お願いします！！

Scientists **complain about noise **pollution. It damages animals, plants, and people. animals and plants need beautiful music. But they don't like big, *4terrible noises. 学習日 9) The Magic of Music 音楽の不思議な力カ 1 The history of music is very old. People all over the world have always loved it s there anyone who doesn't like music? Probably the answer is no. Music is one of the most necessary things in life. Maybe people can't live without music. Do animals and plants like music, too? Do they understand music? 5 2 Oneday Mrs. Evans read a very interesting story in the newspaper. A *1 "university professor found out that her plants became stronger when music was played for them. At first she thought thatit was a joke, but she wanted to try it 2) herself. She built two rooms in the garden and put the same kind of vegetables in both rooms. The temperature of the rooms was the same and both of them were very quiet. Music was played in one room. The other room was silent. She was 3) 10 surprised to find that the next day the vegetables that she played music for became taller than the ones in the silent room. 3 In the United States, there was a farmer who kept many cows. The farmer was very interested in music. When he stayed at home, he always listened to music on the radio. One day he took his radio to the farm. When he was *2milking his cows, 15 the radio was playing beautiful music. He found that the cows gave more milk *than 1usual on that day. He wanted to know the reason, and three months later he 4) learned that he could get more milk when the cows listened to beautiful, quiet music. 4 Today many scientists say that animals and plants also enjoy music. Like Us, 20 *4 *5 They say that we must think about many kinds of noises we are making every that We day. 1 313 words I

この証明問題の解き方を教えて欲しいです、よろしくお願いします

lim (1+z)= = e, 2→0-0

数学の質問です この問題の⑶なんですが、ノートのようなやり方ではダメでしょうか？ ちなみに右ページ青マーカー上から左ページ青マーカー下の順で読み進めていただきたいです 見辛かったら、返信欄にあらためて載せます お願いします🤲

224.〈関数方程式と微分係数) 微分可能なxの関数 f(x) が任意の実数 x, yに対して次の関数を満たす。 f(-x)= -f(x) {f(x)}?+{f(x)}?=1 f(x+y)= f(x)f(y)-f(x)f(y) f(0) =1 (1) f(0)を求めよ。 (2) f(x) は偶関数であることを証明せよ。 (F(2)-f(カ)%=D-2,f(2)(2)を証明せよ。 U-V (4) f'(x) が微分可能であることを示し, f"(x) = -f(x) を証明せよ。 [20 鳥取大·医,I)

数学の質問です この問題の⑶なんですが、ノートのようなやり方ではダメでしょうか？ ちなみに右ページ青マーカー上から左ページ青マーカー下の順で読み進めていただきたいです 見辛かったら、返信欄にあらためて載せます お願いします🤲

224.〈関数方程式と微分係数) 微分可能なxの関数 f(x) が任意の実数 x, yに対して次の関数を満たす。 f(-x)= -f(x) {f(x)}?+{f(x)}?=1 f(x+y)= f(x)f(y)-f(x)f(y) f(0) =1 (1) f(0)を求めよ。 (2) f(x) は偶関数であることを証明せよ。 (F(2)-f(カ)%=D-2,f(2)(2)を証明せよ。 U-V (4) f'(x) が微分可能であることを示し, f"(x) = -f(x) を証明せよ。 [20 鳥取大·医,I)

微分の問題(2)と極限値の求め方がわかりません 極限値は通分してからがどうなるか分からないので教えて下さい

(1) zV4-22 +4sin-1 2 1- sin (2) log V1+ sin z

3行目のbroughtがなぜpeopleを修飾するものになるのか教えてください！！

TW 9189 ⑤ The novelist presents us with people. He tells us what kind of people they are, whether they are good, bad, or indifferent. Within the limits of a book he tells us what happens to the people brought to our attention. The story depends on what they do, and particularly what they do in relationship with each other. LOMT auLr Sug G: V STe co ngldo

このページ分からなすぎて手につきません(＞＜) 誰か優しい方教えてくださいm(_ _)m

JEB2A1-P1A3-01 20-SAJ9-1ASeし いてのレポートを, B. では、 Kumiko がアメリカ滞在についてのレボートを書いていて これらを読んで, あとの設問に答えなさい。Jま (配点 25) itnoieil 970W NDO ode 800 A. Alice's Report other family is a big ① one. This is Judy. She is my cousin*. She lives in England.She has a smal family. She lives with her father, mother and sister. They live in an apartment*. Judy's grandparents* live far away. Judy and her family visit VTTI them once a year. Won juo ar oda This is Roberto. He is my pen pal*. He lives in Chile*. He has a big family He lives with his father, mother, brothers, sisters and grandparents. They live in a big house. His aunt, uncle and cousins live in a house next door. They see each other every day. Swon one at s19dW MPCU 12 aps Rom& ro courG pGLGS B. Kumiko's Report g6229m 6 9V69lIns Last year I stayed with an American family, I lived with the Green family in the state of Texas*. I went to school with my American sister, Cindy. At first English was very (② ) and I was homesick*. But Mr. Green, Mrs. Green and Cindy were very kind. I studied English very hard. School was interesting. I enjoyed life in the United States. Now I'm in Japan. I often write to my American family and they write to me. Next year the Greens are going to visit me. 101ood odd ot (6Wani om iloT (注) cousin= いとこ apartment= アパート (マンション)0ds woH grandparents=祖父母 pen pal= 文通相手 Chile= チリoidW the state of Texas= テキサス州 homesick=ホームシックの (1) 下線部①の one が指すものを, 本文から抜き出して1語で答えなさい。

この問題の解説お願いします。至急です💧

51 b=(-1)"-! log n+2 (n=1, 2, 3, …) で定められる数列(b.} に対して. n Sn= bi+ b2+…+bn とする。このとき, lim Sn を求めよ。 Clear- (08 岡山大) n→0

線の引いてあるところで、なぜそのような関係になっているのでしょうか？ その関係はどの式からわかりますか？ よろしくお願いします

11 漸化式と極限 Example 11 *★★** (n=1, 2, ………) で定められる数列{an} がある 2 3 an a=3, an+1 an 不等式 a,>V6 を証明せよ。 不等式 a-6く (an-16)? を証明せよ。 (17 大阪府大) ( lima, を求めよ。 key 数学的帰納法で示 解答(1) [1] n=1 のとき, a=3>V6 より成り立立つ。 [2] n=k のとき、 ax>V6 が成り立つと仮定すると す。 V6=(a-/6)。 2ak a4+1-/6=+6 よって、n=k+1 のときも成り立つ。 [1]. [2] から,すべての自然数nについて an>V6 終 - 2ak (2) 2<、6<a。 であるから G-/5-(an-/6)<(an-16_1(an-/6)* 国 *今母が在の方が大きくなる。 2a。 2-2 (3) b,=a,-V6 とおくと, (2) から key (2)の不等式を繰り 返し用いて、はさみうち この関係式を繰り返し用いると, n22 のとき 0くん、くーのぷく合めざく の原理を利用。 424-1」6,24-1 16|-|3-6<1より lim b"=0 であるから、 2月-1 はさみうちの原理により lim b,=0 月→ 00 すなわち lima,=(6

基礎解析です、この2問がわかりません　

[4] ICRを区間,f:1→R, a€1とする。以下の2つが同値であることを示せ。 (i) fはaで連続 (i) lim a, = aと Vn € N, a, elを満たす任意の数列{r,}」に対して lim f(z,) = f(a)が成り立つ。 [5] 1,KCRを開区間,af0とする。f:I→RはIで微分可能とし,g:K→Rは 9(z) = azで定め, g(K) cIであるとする.p:K →Rを(z) = f(g(z)) で定めた とき,ゅの導関数をfの導関数f' とaを用いて表せ、