学年

質問の種類

数学 高校生

この解説の(2)(3)がよく分からないので教えて欲しいです!

144 第6章 微分法と積分法 基礎問 90 共通接線 5/5 2つの曲線 C: y=x3, D:y=x2+pr+g がある (1) C上の点P(a, d3) における接線を求めよ (2) 曲線DはPを通り,DのPにおける接線はと一致する。こ のとき,p,q をαで表せ) 小 (3) (2)のとき, D軸に接するようなαの値を求めよ。 (2)2つの曲線 C,Dが共通の接線をもっているということです が,共通接線には次の2つの形があります 精講 (I型) (Ⅱ型) y=f(x)=g(x)y=f(x) y=g(z) Qi P アイは一致するので, 3d²=2a+p, -20°=q-a 1, p=3a²-2a, q=-2a+a² y = ( x + 2² )² + q = b² だから, 曲線 (3) D:y=(x+ 4 Dがx軸に接するとき,頂点のy座標は 0 . -=0 4 4q-p²=0 よって, 4(-2a3+α2)-(3a2-2a)=0 4a²(−2a+1)-α(3a-2)2=0 a^{-8a+4-(9a2-12a+4)}=0 a³(9a-4)=0 <x²+px+q=0 の 145 (判別式) =0 でもよい 展開しないで共通因数 でくくる 4 .. a=0, 9 注 a=0が答の1つになること は,図をかけば軸が共通接線 であることから予想がつきます. 20 YA C 10 (2)はポイントを使うと次のようになります。 a α 違いは、接点が一致しているか, 一致していないかで,この問題は接点がP で一致しているので(I型)になります。 小 入 どちらの型も、接線をそれぞれ求めて傾きとy切片がともに一致すると考え れば答をだせますが, (I型)についてはポイントの公式を覚えておいた方が よいでしょう. 解答は,この公式を知らないという前提で作ってあります. 解答 (1)y=xより,y'=3m² だから,P(a, α) における接線は, y-a³=3a²(x-a) :.l:y=3ax-2α° ......ア C (2)PはD上にあるので,a+pa+g=a ...... ① PEDESTA 86 また,y=x+px+α より y'=2x+pだから,ませ Pにおける接線は,y-a=(a+b)(x-a) :.l:y=(2a+p)x+α-202-pa y=(2a+p)x+q-a² ......(*) y-f(t) f(x)=x, g(x)=x+px+g とおくと f'(x)=3x2, g'(x)=2x+p [ a³=a²+pa+q 13a2=2a+p p=3a2-2a よって, g= -2a3+α2 ポイント 2つの曲線 y=f(x) と y=g(x) 共有し, その点における接線が一致する f(t)=g(t) かつ f'(t)=g'(t) 点 (t, f(t)) を 演習問題 90 第6章 関数 f(x)=x^2とg(x)=-x+αのグラフが点Pを共有 し、点Pにおける接線が一致する。このとき,aの値とPの座標を 求めよ. Inn Hml

解決済み 回答数: 1
英語 高校生

英語の長文です 文法表現があるところが知りたいです!

UNIT 5 Reading Passage 5 10 15 20 20 25 Listening There is a saying in France that states: "The government could fall, the Louvre¹ could be broken into, or aliens could land on Earth, but if any of these things happened during the Tour de France, no one would notice." The Tour de France is the most famous cycling race in the world. The which is held in July every year, consists of twenty one-day stages, plus several rest days. The course follows a clockwise route around France, and often neighboring countries, including Luxembourg, Belgium, and Italy. The winner is the rider who completes all twenty stages of the race in the shortest overall time. race, The Tour de France first started on July 1, 1903, when sixty cyclists left from in front of The Alarm Clock Café, just outside of Paris, and rode 467 kilometers to Lyon. The first race consisted of six legs, each of which was about 400 kilometers long. At that time, there were no rest days the winner was the rider who finished the race in the shortest total time. The winner of the first Tour de France, Maurice Garin, the most popular cyclist in France at that time, received 2,000 francs (about $350). It took him 94 hours and 33 minutes to ride all 2,428 kilometers of the race, three hours faster than the runner-up.² Over the weeks during which the race was run, the idea of the Tour de France slowly caught on with the people of France. The race has been held every year since that time, except during the years of World Wars I and II.³ The Tour de France has developed several special honors for which racers compete. The highest honor is the "yellow jersey." Henri Desgranges, the founder of the race, introduced the yellow jersey in 1919 to show the leading racer each day of the Tour de France. Each day, the officials who keep track of all of the riders' times compare each rider's total time up to that point. The racer with the lowest overall time wears the yellow jersey during the following day's race. Other honors include the "green jersey," which is given to the best sprinter, and the "polka dot jersey," a white jersey with red dots, for the best rider in the mountains along the route. Over the years of the race, the competitors have gained a reputation for good sportsmanship. For example, if a lead rider falls off his bike, it is common for the following riders to slow down to allow the fallen rider to catch up. Some watchers are surprised by this, but as German rider Jan Ullrich, who came in runner-up in 2002 after waiting for winner Lance Armstrong, says, "Of course I would wait. If I would have won this race by taking advantage of someone's bad luck, then the race was not worth winning." 1 the Louvre a famous museum in Paris 2 runner-up someone who comes second in a race or other competition 3 World Wars I and II 1914-1918 and 1939 - 1945 abent ages

回答募集中 回答数: 0