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Mathematics Senior High

この問題のf(x)の増減表は何のために求めているのですか?

基本 例題 155 曲線 F(x, y) = 0 と面積 良介 曲線 2x2+y+y2=1 によって囲まれた部分の面積Sを求めよ。 .88 CHART & SOLUTION 曲線 F(x, y) = 0 と面積 y=(x の式)と変形したグラフを考える 重要 88, 基本 152 与えられた曲線の方程式を y=f(x)の形に変形し、定義域や増減を調べてグラフをかく。 対称性も利用する。 [注意]x軸対称: f(x, -y)=f(x, y) 軸対称: f(x,y)=f(x,y) 原点対称: f(-x, -y)=f(x, y) 解答 2x2+2xy+y2=1から y2+2xy+2x2-1=0 80-1200-1 yについて解くと y=-x±√x2-(2x2-1) =-x±√1-x2 015030020 f(x)=-x+√1-x2, g(x)=-x-√1-x2とする。 1-x2≧0 であるから, f(x) g(x)の定義域は √1-x2+x -2x f'(x)=-1+ 2√1-x2 f'(x) =0 とすると √1-x2=-x 両辺を2乗して 1-x2=x2 よってx=±1/1 ① yについて整理し,解の 公式を用いて解く。 a (1200-1)D=x (1-x2)={(1-x2)/2 =1/2(1-x2)-12(1-2) 10 ① を満たすものは x=-- √2 f(x) の増減表は右のようになる。 また g(-x)=-(-x)-1-(-x)^ x -1 f'(x) √21 + 0 1 極大 f(x) 1 > > √2 -1 247 =x-√1-x2=-f(x) thaia よって, y=f(x) のグラフと y=g(x) のグラフは原点に 関して対称であるから, 曲線の概形は,図のようになる。 定義域内では,f(x)≧g(x) であるから, 求める面積Sは S=S_{f(x)-g(x)dx=21-xdx. -x21 Sixx は、半径1の円の面積の1/2を表すから S=2.12- =π 2 y=f(x)2 -1 0 Caar -17 とで 1 で表し 1 y=g(x) x

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Mathematics Senior High

答えが無くて、あってるかどうか添削してください

① ( )内から最も適切な語句を選び,○で囲みなさい。 1. She had her mother (pack / packed) some sandwiches. 2. I hate (his/he) being treated like that. his 3. I'm sorry for (not going / going not) to the party. 4. He is proud of (buying / having bought) the house when he was young. 5. I heard the birds (to sing / singing). 2( 内に入る最も適切な語句を選び, 番号を○で囲みなさい。 1. Dad, if my grades improve by the end of the term, would you mind ( 34678 2 locking ) by my nickname. raising 2 rising 3 to raise 4 to rise 2. "I'd better call our neighbor to ask her to check the door of our apartment." "You don't have to do that. I remember ( ) it when we left." 1 lock 3 to be locked 3. I like ( 1 call 1 allowed 2 being called 4. "Our trip to Tokyo was fun, wasn't it?" "Yes, it was great! I'm really looking forward ( 1 go 2 going 3 5. "Do you still plan to go to Hawaii this winter vacation?" "Yes, and I wish you'd consider ( ) with me." 1 go 2 going 3 to go 6. If the pain in your throat becomes worse, have it ( 2 checking 1 check 3 to check 7. Although her parents had said "no" for a long time, they finally ( alone. 3 to call ->>> 1 2 5 8 10 ) at once. ) my allowance? 〔センター試験〕 4 to lock 4 calling ) there again sometime." [センター試験〕 to go 4 to going 4 to going [センター試験〕 4 checked 4 made 〔センター試験〕 [センター試験] ) her go to Europe 〔センター試験〕 2 got 3 let 3 ( 内の語句を並べかえて, 意味の通る文にしなさい。 1. I was thinking of the speech (called, I had to, make, my name, when I heard ). [センター試験] I was thinking of the speech I had to make when, I heard 2. If we want to (English, in, make, ourselves, understood ), we need not only good language skills but also clear thinking and a broad general knowledge. If we want to make ourselves understood in English language skills but also clear thinking and a broad general knowledge. [センター試験] we need not only good 02.01

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