この問題が解けません。 aを満たすところが意味がわかりません。

Question 2. (10 Points) Give me a graph, where the z's all laugh, and play by the following rules On the figure below, sketch the graph of a function y = f(x) that satisfies: (a) lim f(z) = 3, (d) lim f(z) = 5。 エ→1+ lim, f(x) = 0. (e) lim f(z) =-5, エ→1- (c) lim f(z) = -8 (f) f(1) = 2, and エ→ (g)f is defined everywhere except maybe z =-3. 6 2 -6 -4 -2 2 4 6 -2 -4

どうして3番が答えなんですか？

15, 富士山に登るつもりなら、その靴は修理する必要がある。 If you intend to climb Mt. Fuji, these shoes want ( の to repair ② to have repaired The ③ repairing ④ being repaired 16) アメリカのほとんどの地域で、昔に比べてボ

この問題わかる方居たら回答して欲しいです。 よろしくお願いしますm(._.)m

④ Choose the suitable one. [→L.14] (1)( Climb / Climbing) the mountain was a wonderful experience for us all. (2) The little girl insisted on ( wearing / to wear) the red shoes. (3) I' m sorry for ( arriving / not arriving ) soon enough. The bus was late. (4) Would you mind ( picking me / me picking ) up on the way? (5) Would you mind ( using / me using) your bike? I' ll return it soon. (6) I finished (preparing / to prepare ) for the school trip at midnight. (7) He refused ( accepting/ to accept) that there was a serious problem. (8) You are the last person, so don' t forget ( turning / to turn ) out the lights. (9) My sister remembers ( visiting / to visit ) Okinawa when she was four. (10) She hopes ( being / to be ) successful in the exam. (11) My uncle gave up ( teaching / to teach ) three years ago. (12) They stopped ( watching / to watch) the drama when the doorbell rang

この問題の問題13-1（3）（4）、問題13-2の解答を作ってください！ お願いします！

2021年 物理学演習2 第13回 デルタ関数 関数f(x)がどのような関数であっても次のような関係を満たす8(x) をデルタ関数という。 「r86) = f0) JO (x * 0) l0(x = 0) 8(x) = このデルタ関数は物理学者の P.A. Dirac によって発明された。名前に関数とついているが、正確 には関数ではなく汎関数の一種の超関数で、線型性と連続性などを満たした汎関数である。 関数: 数 → 数 例えば x → y=f(x) 汎関数:関数 → 数例えば f(x) → f(0) = Sf(x)6(x)dx デルタ関数は関数では無いが、実際には下記のような関数の極限とみなすことができ、どの表現も 同等である。 8(x) = lim 8,(x), ど→+0 8,(x) = {o (x> £/2) 1 28 8(x) = lim 8,(x), E→+0 6,(x) = 2x?+ 2 1 8(x) = lim 8,(x), ど→+0 6(x) = e VTE 8(x) = lim 8,(x), 1 8,(x) = 「e-ddk Zt J-o 1(x2 0) lo (x < 0) 8(x) = 0'(x), 0(x) = 3次元のデルタ関数は以下のように1次元のデルタ関数の積になる。 8(r) = 6(x)6(y)8(z) (o (x =y=z= 0) lo (x =y=z=0以外の場合) 8(r) = 問題13-1 f(x)はx| → oで0となるなめらかな関数とする。デルタ関数8(x) f(x)6(x - a)dx= f(a) について次の性質を証明しなさい。 (1) x6(x) = 0 (2) 6(ax) = )(a>0) (3) 6(x) = 0°(x) so (x< 0) l1 (x> 0) 0(x)は階段関数(ヘビサイド関数)であり、e(x) = である。 {8(x - a) + 6(x + a)}(a> 0) 問題13-2 正規分布を表す次式 = (x)9 がa→ +0 のときにデルタ関数となることを証明しなさい。 1 -exp V2To 2g2

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5 次の英文を読んで, 設問に答えなさい。 Forty-two kilometers is a long way to run without stopping. But twenty-thousand *competitors with a lot of energy try to do that everv vear in the Boston Marathon. The race is the oldest marathon in the world held each year. Men and women aged eighteen and over run in the marathon. Some competitors are much older than eighteen. Some runners are seventy 1) and older. But most of the nunners are younger than forty. 5) Winners share five-hundred-twenty-five-thousand dollars in prize money given by companies and organizations. Runners in the Boston Marathon have shown that they are good at the sport. They completed earlier marathon races called *qualifying races. They had to run those races withina set time. Other people join the Boston Marathon just for fun. these people have not officially joined the race. They just start running with the crowds. They are called "bandit." Many of them probably will finish hours after the serious runners. But these unofficial racers are just happy. They sometimes kiss the ground after crossing the finishing line. Before the marathon begins, a *computer chip device is attached to each runner's shoe. It electronically records the runner's time. Timing begins when a runner passes another device placed across the road at the starting line. The computer chip records each runner's time as he or she 10) passes several points along the race. It records the runner's final time when crossing the finishing line. Running has gained popularity for several reasons. You can do it anywhere, any time. You do not need other people, and you do not need much *equipment. However, experts say you should wear a good pair of running shoes to protect your feet. The manufacture of running shoes has become a huge industry. 15) (注):competitors 競争者, 谷 qualifying races 参加資格選考レース ftow ol jcaw yilnot computer chip device コンピューターチィップ装置、 equipment 装備 m ow o1 sVed I ( Tmm ow vami (下) 次の英文(ア)~(ソ)の中から, 本文の内容と一致するものを5つだけ選びなさい。 (lo buid ev adT (T)(5) 問 ab gnidaaw ucoM (マ) (ア)Boston has held a marathon each year longer than any other city has. ood l I () 5 解答欄 各6点 d a V bastl yod d aw The number of competitors in the Boston Marathon is limited to no more than ten-thousand. T. (ウ)Competitors in the Boston Marathon are at least eighteen years of age. Vab balbom (エ) The majority of the runners in the Boston Marathon are over forty years of age. bad d (オ) The winner of the Boston Marathon receives five-hundred-twenty-five-thousand dollars in prize money given by companies and organizations. xe (カ)Some of the official runners in the Boston Marathon have never run a marathon before. ld (キ)In order to officially enter the Boston Marathon, a runner must run a qualifying race within a set time. (ク)The people who join the Boston Marathon just for fun register one hour before the race. (ケ)Most of the unofficial racers are much faster than the serious racers. pbo dh al oinogiojeg olmd boresvan nis nd aT (コ) The unofficial runners sometimes kiss the ground after crossing the starting line. (サ)A computer chip is attached to each runner's shoe to record electronically the time it takes a runner to run the race. (シ)The only times recorded are the starting time and the finishing time. 00 lod lt (ス) Unofficial runners are often happy because they get better chips in their shoes than official runners get. (セ)The recording of the race time starts when the runner crosses the starting line. id bot odo od (ソ) Running has gained popularity for only one reason.

数Ⅲ　青チャート　例題131　（１） の問題の質問です 写真の赤のライン所はいりますか？　もしいるとしたら　なんのためにあるのですか？

222 基本 例題 131 関数の片側からの極限 x-2 lim lim x→1-0 X-1 x-2 を求めよ。 x*-x の極限は存在するかどう lx| x→0のとき, 関数 指針> (1) x-→1+0, x→1-0のどちらの場合も x-1→0となるが, その符号は近づき方によって 異なることに着目。 (2) a20のとき lal=a, a<0のとき |a|=-a 右側極限(x→ +0), 左側極限(x→-0) を調べて 一致すればそれが極限,一致しなければ極限はない とす に注意。 解答 (1) x→1+0のとき x-1→ +0, x-2→-1+0 よって x-2 lim エ→1+0 X一-1 また, x→1-0のとき x-1→-0, x-2→-1-0 よって lim x-2 三の *→1-0 X-1

数II 微分係数 一番の問題がさっぱりわかりません。 教えてください！！

型 1 1 次のO, 2, ③を満たす整式f(x) のうち, 次数が最も低いものを求めよ。 f(x) lim =4…① x→1 X-1 lim(x) x→2 X-2 lim/(t) x→3 X-3 =-3…② -=12…③ 2 関数f(x)=x°-6ax?+3a’x+5 (aキ0) において, (極大値)-(極小値) の値が 32 古

微分の問題です。(2)の途中式と説明もお願い致します。

ロピタルの定理が使える理由を述べ,ロピタル の定理を使い極限を計算しなさい。 1 (1) lim z°e-ェ エ→0 (2)/ lim エ→。 (2r - 1)(2 + 3)2 - 4Tan-12

(1) (4) の解き方教えてください！

48 次の極限を求めよ。 5"-3" 4 lim 2"-1

問4① 彼らは少ない時間でより生産的になる、というのが仕事に対して言っていると特定できるのは何故でしょうか、、、？？ 本文で生産的になるのが仕事のことしか言っていないからでしょうか？？

第3回 実戦問題 73 Vou are going to have a debate about men taking parental leave. In order to prepare for the debate, your group is reading the article below. According t0 a recent survey, about 5.14% of new fathers in Japan Love taken parental leave. Over the years, the number of men who take 18u0 narental leave has grown, but it is still a big challenge for men to take it in male-oriented-Japanese society. So, here is my question: Do you think more Japanese men should take parental leave or not? Taking parental leave has one great benefit. If men take it for even a couple of weeks after the baby arrives, it is a great help to their wives. Most families are now nuclear families, so it is more difficult for couples with a new child to get support from their parents. Husbands can provide not only physical support but also mental support to their wives. Since new mothers face many unexpected situations every day, they can feel a lot of stress. Getting help is the key to reducing it. Another benefit is that parental leave is usually refreshing for men, allowing them to work more efficiently after they return to their jobs. On the other hand, there are reasons men should not take it. (First, during parental leave, they get no salary. This can put a lot of pressure on family finances. Second, many people are still against men taking it, which places psychological pressure on the men who do. What do you think about this issue? Ibelieve that when men take parental leave, it helps them understand how hard caring for a baby is. Knowing more about the hard work of their wives surely strengthens their relationship. Furthermore, when men eagerly raise their children, Tamily bonds become stronger. Nobody could argue that such things should be not be encouraged. 第3回 don