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数学 高校生

大問105だけ、はさみうちの原理使ってるんですけど、使うときと使わない時の判断ってどうやってるんですか?式のどの部分を見たら「はさみうち」使って解く!って分からんですか?

第2章 極限 三角関数と極限 1 関数の極限と大小関係 limf(x) =α, limg(x) =β とする。 xa pix 1 xがαに近いとき,常に f(x) ≦g(x)ならば a≦β 2xがαに近いとき,常に f(x) (x)g(x) かつα=β ならば limh(x)=a 注意 上の事柄は,x→∞, x→∞の場合にも成り立つ。 ■ 次の極限を求めよ。 [104, 105] 1-cos 3x □ 104(1) lim x→0 x2 1 *105(1) limxcos 0+x x 第2節 関数の極限 31 0 (2) lim sinx2 x01−cosx (2) lim 1+sinx XII∞ x 第2章 極限 注意2を「はさみうちの原理」 ということがある。 例題 3 limf(x)=∞ のとき,十分大きいxで常に f(x)≦g(x) ならば limg(x) =∞ |2 三角関数と極限 sinx lim x0 x x =1, lim -1 (角の単位はラジアン) x-0 sinx STEPA 中心が 0, 直径 ABが4の半円の弧の中点をMとし, Aから出た光線 が弧 MB 上の点Pで反射して, AB上の点Qにくるとする。 (1) 0=∠PAB とするとき, OQ の長さを0で表せ。 (2) PBに限りなく近づくとき, Qはどんな点に近づいていくか。 |指針 Aから出た光線か MB上の点Pで反射して, AB上の点Qにくるとき ∠OPA = ∠OPQ sin O 求めるものを式で表し、 などの極限に帰着させる。 解答 (1) 右の図において ✓ 99 次の極限を調べよ。 ZOQ= ∠OPA=∠OAP=0 ∠PQB= ∠PAQ+ ∠APQ=30 M 2 (1) lim cos- *(2) lim (3)lim x tanx x–0 sinx よって ∠OQP=30 △OPQに正弦定理を用いると,P=2 であるから 30 0 Q B ■次の極限を求めよ。 [ 100~103] ✓ 100 (1) lim x→0 sin 4x XC sin2x *(2) lim x-0 sin5x (3) lim x-0 tant sin3x tan2x-sinx □ 101 (1) lim- *(2) lim x→0 x 1-cos 2x x-0 xsinx (3) lim x→0 sin3x+sinx sin2x □ 102(1) lim COS X x-Sin2x (2) lim- sin2x (3) lim x01−cosx 103*(1) lim tan x X10 x *(4) lim- sinлx x-1 x-1 1−cosx t- sinx STEPB *(2) lim X→π OQ 2 sin O sin(-30) また, sin (π-30)=sin30 であるから 2sin OQ= sin 30 (2)PがBに限りなく近づくとき, 0 +0 である。 このとき 2 sin 2 sin 3 2 lim OQ= lim lim 8+0 o sin 30 0-40 3 0 sin 36 3 よって,Qは線分 OB上の0からの距離にある点に近づいていく。圏 □ 106 半径αの円周上に動点Pと定点Aがある。 Aにおける接線上に AQ=AP であるような点Qを直線OAに関してPと同じ側にとる。PがA PQ に限りなく近づくとき, AP の極限値を求めよ。 ただし,Pは ∠AOP (0<< AOP < 1)に対する弧AP の長さを表す。 sin(x-7) x-π (3) lim x-- tanx xn ax+b 1 sin(sinx) (5) lim x→0 sinx 1 107 等式 lim (6) limxsin COS x 2x が成り立つように, 定数a, b の値を定めよ。

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数学 高校生

vision questⅡ English expression hope70ページ preview 1.date&time 2.numbers(sizes,measurements,etc) 3.prices&Phone numbers listening task 1.... 続きを読む

140 // TIT Activity for Communication 3 Preview Listen to the sentences below. 1 Dates & Times Listening for Numbers the on Enio 1. "The movie starts at 5:20. Can you be ready in ten minutes?" "OK. I'll try." 2. "What time is it now?" "It's 11:30." basalaila awohlsw 3. I have an appointment with the dentist this Thursday, the 10th. M 4. "When does school begin?" "It begins on April 8th." 5. Our school was established in 1965. 6. My family has lived in this town since 2005. 2 Numbers (sizes, measurements, etc.) 1. Two thirds of the students come to school by bus. 2. One mile is about 1,609 meters. 3. The city has a population of about 2.5 million. 4. The temperature dropped to 12°C. 5. APA Air Flight 125 for London will be departing from Gate 14 at 10:15. 3 Prices & Phone numbers 1. The price of this bag is $27.89, but you can have it at 10 percent off. 2. What would you do if you won 100 million yen in a lottery? 3. "A hamburger and a cola, please." "That'll be £2.99." 4. I need €20, but I'm €5 short. 5. My phone number is 612-750-5613. Listening Task Listen to the conversations and choose the correct answers. 1. How much of the earth's surface is covered by ocean? 1 more than one third more than one fourth 監督署 ER 70 3 more than two thirds 4 more than two fifths 2. When were the Olympic Games held in Atlanta? 1 in 1966 2 in 1969 3. How much did the dress cost? 1,100 yen 2 1,800 yen 3 in 1996 4 in 1999 S 8,000 yen ③ 13,000 48,800 yen bluros ④ 30,000 about 200,000 4. How many people can the concert hall hold? ① 1,300 ② 3,000 5. How many people live in the city? ①about 2,000 2 about 12,000 3 about 20,000 ① 207-7300 2207-7003 ③ 702-3300 6. What's the phone number of the restaurant? The number is 510- ④ 702-3003

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英語 高校生

vision questⅡ English expression hope70ページ preview 1.dates&time 2.numbers(sizes,measurements,etc) 3.prices&Phone numbers listening task 1... 続きを読む

140 // TIT Activity for Communication 3 Preview Listen to the sentences below. 1 Dates & Times Listening for Numbers the on Enio 1. "The movie starts at 5:20. Can you be ready in ten minutes?" "OK. I'll try." 2. "What time is it now?" "It's 11:30." basalaila awohlsw 3. I have an appointment with the dentist this Thursday, the 10th. M 4. "When does school begin?" "It begins on April 8th." 5. Our school was established in 1965. 6. My family has lived in this town since 2005. 2 Numbers (sizes, measurements, etc.) 1. Two thirds of the students come to school by bus. 2. One mile is about 1,609 meters. 3. The city has a population of about 2.5 million. 4. The temperature dropped to 12°C. 5. APA Air Flight 125 for London will be departing from Gate 14 at 10:15. 3 Prices & Phone numbers 1. The price of this bag is $27.89, but you can have it at 10 percent off. 2. What would you do if you won 100 million yen in a lottery? 3. "A hamburger and a cola, please." "That'll be £2.99." 4. I need €20, but I'm €5 short. 5. My phone number is 612-750-5613. Listening Task Listen to the conversations and choose the correct answers. 1. How much of the earth's surface is covered by ocean? 1 more than one third more than one fourth 監督署 ER 70 3 more than two thirds 4 more than two fifths 2. When were the Olympic Games held in Atlanta? 1 in 1966 2 in 1969 3. How much did the dress cost? 1,100 yen 2 1,800 yen 3 in 1996 4 in 1999 S 8,000 yen ③ 13,000 48,800 yen bluros ④ 30,000 about 200,000 4. How many people can the concert hall hold? ① 1,300 ② 3,000 5. How many people live in the city? ①about 2,000 2 about 12,000 3 about 20,000 ① 207-7300 2207-7003 ③ 702-3300 6. What's the phone number of the restaurant? The number is 510- ④ 702-3003

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