求解第5題

PROPERTIES OF CURVES (Chapter 13) 340 ACTIVITY Click on the icon to run a card game on curve properties. REVIEW SET 13A b y = x - 5x + 2 at (2,0) 1 Find the equation of the tangent to: a y=-222 at the point where x = -1 1-2x at (1, - d f(x) = (3x-1 at the point where 1 = e f(x) = ln(x-2) at the point where x = e. 2 Find the equation of the normal to: a y = 13.1 +4 at (4,4) y = 3e2: a Find a. b at the point where I = 1. 3 At the point where x = 0, the tangent to f(x) = 4x + px + q has equation y = 50-1 Find p and q. 4 Find all points on the curve y = 22 + 3.22 - 10x +3 where the gradient of the tangent is 2 5 The line through A(2, 4) and B(0,8) is a tangent to y= (x + 2)2 6 Find where the tangent to y = 228 +4x – 1 at (1,5) meets the curve again. a Find the equation of the normal to y = e2c at the point where x = a. b Hence find the equation of the normal to y = e21 which passes through the origin. 8 Find the coordinates of P and Q if (PQ) 5 y = at (1,5). va 7 YA is the tangent to P (1,5) 5 y = Q The tangent to y = x+/T = c at * = -3 cuts the axes at points A and B. Determine the area of triangle OAB. Find intervals where f(x) = -23 - 6x2 + 36x - 17 is: a increasing Consider the function f(x) = 2x3 - 3x2 - 360 +7. a Find and classify all stationary points. b decreasing b Find intervals where the function is increasing and decreasing. Describe the behaviour of the function as 200 and as X-→ -0. d Sketch the graph of y=f(x) showing the

這大題求解

II、綜合測驗:20% There are only a handful of underwater hotels around the world. These 16. guests to do what few people ever dream of doing: sleeping underwater. Fish, of course, do this all the time, but to humans the thought of 17._one's head on the seabed isn't very appealing. That's because mammals like us 18. have sufficient air to breathe. 19. _ ever wondered, therefore, how sea mammals, like whales, manage to get their beauty sleep? A number of 20. have attempted to answer this question. They seem to suggest that whales make use of an 21. sleep technique known as “logging.” During "logging," whales are 22. to shut down just one half of their brains. This enables them to get some much-needed rest, and yet at the same time remain alert enough to regularly return to the surface of the water to breathe. 23._ another sea creature that makes use of “logging" to survive is the dolphin. _24. Whales, which can remain underwater for up to ninety minutes, dolphins need to breathe in fresh air above the surface every twenty minutes. Thus for them it's even more important to keep half their brains awake at all times. Logging helps them 25. this. At the end of the day, this is just another example of how human and animal sleep habits are different in strange yet wonderful ways- ( ) 16. (A) let (B) allow (C) make (D) have ( ) 17. (A) throwing (B) burying (C) laying (D) lying ) 18. (A) must (B) may (C) can (D) will ( ) 19. (A) Will you (B) Do you (C) Are you (D) Have you ( ) 20. (A) secrets (B) habits (C) studies (D) facts ) 21. (A) amazed (B) amazing (C) amaze (D) amazingly ( ) 22. (A) able (B) possible (C) capable (D) likely ) 23. (A) Just (B) So (C) Also (D) Yet ) 24. (A) As (D) Unlike ) 25. (A) achieving (B) achieve (C) be achieved (D) to achieving (B) TO (C) With V. 文意選填:10%(請忽略大小寫) A) in fact (B) however (C) amazing (D) standing (E) much Animals sleep in incredible ways. They don't need to lie in bed for hours like we do. Zebra phants, for example, can stay 26. while they sleep. This odd sleeping position comfortable, but it's 27. safer. Predators are always around to catch sleepy prey a phants, therefore, are only away in dreamland for around 3.5 hours a day. Zebras are reported a less. Giraffes, 28. sleep the least of any animal. An average of half an hour per day is hey need to survive in the wild. 29. they hardly ever sleep for more than five minutes af fost and for less than an hour a day?

求解1. b

B 3 Investigation 1 When a curve is increasing, we say that it has a positive gradient, and when it is decreasing we say that it has a negative gradient. Consider the curve y=xº shown in the diagram. 1 a Give the range of x values for which the gradient of the curve is i negative I ii positive iii equal to zero. b At which point is the gradient of the curve greater. A or B? The tangent to a curve at a point is the straight line that just touches but does not cross the curve at that point. N 1 y=p 1 2. 3 2 2 a On your GDC or other software, plot the curve y=x' and draw the tangent at the point (1, 1), as shown in the second diagram. b Zoom in to the point (1, 1). Factual What do you notice about the gradient of the tangent and the gradient of the curve at the point of contact? c Use your GDC or online software to draw tangents to y=x' at the points listed below and in each case write down the gradient of the tangent. 0 -1 1 2 X -1 0 2 2. 3 Gradient of tangent at x 2 d Conjecture a function for the gradient of y = x2 at the point on the curve with coordinates (x,x).

第3題求解！🙏謝謝~

256 225 225 With Pencil } ( ) 3. 學校樂團成果發表晚會,預留一排有8個座位的貴賓席,當天一對貴賓是夫婦, 12 表示兩人會準時出席,一定會有接待人員帶領,相鄰而坐;另有三位貴賓表示, 因為個人行程緊湊,時間會耽誤,為了不影響節目進行,他們陸續入場後,會各 自任意選擇貴賓席就坐,則表演當天,貴賓席會出現3個空位都不相鄰的機率為 多少? 2 1 3 5 (1) (3) (4) ( (5) 7 7 14 14 14 (2) -53-

求解orz

Supose we know that f(x)=x' +2x+1 has an inverse function f !, Then (f !)'(4)=_7 【中正數學】

求解( ･ั﹏･ั)

wy 若 lim f(x)=b,則 微 Let f be twice differentiable function and let u(x)=f(x²-1) if f'(0)=1 , f"(0) = 2 · then u"(1)=_| 【清華經濟】

微積分的問題，雙倍三倍的概念

27-30 MODELING, APPLICATIONS 27. Exponential growth. If the growth rate of a culture of bacteria is proportional to the number of bacteria present and after 1 day is 1.25 times the original number, within what interval of time will the number of bacteria (a) double, (b) triple?

第三題 想請問各位為何詳解把E的法向量×（-1） 有特殊意義在嗎？ 還是只是比較好看而已？ 謝謝各位！

4 ·L L2 - 4t , 3t-1, 1-2) E 3 30 ) 4x+3/3 2-2 (1)設平面E之法向量 n, 則L=(3,2,4), nl vz=(2,1,1) 4 3 -4 3 n A(3,1, -5) 3 2 又x (1) 9 L, 1 1 1 2 2 =(-2,5,-1) .令n= (2,-5,1)且過點(-3,5,2) .平面方程式為2x-5y+z=-29 L。 0,-1,-2)

有點看不太懂解析寫什麼 求翻譯🙏

er. A SOAL 設了第一套 (4) 1)在首/ 74 - 影片,則 到自旋的阳,雖(Pi)指的套/), ax+by+olo 3. WITH L, : ax + by + c = 0 F Lz : ax + by + c = 0 TL FERI (ZZ)= | la-cal a+b 1 1 fath TW - 1 y=-22- | o 基礎 對稱於x轴、y軸及直線=x O ( 求直線:=2+1對於上朝的對稱圖形方程式為-XL (3求直線! - 2+1等於直線的對稱圖形方程式為-X (2就求直線L:y = 2x + 1 對於軸的對稱圖形方程式為A-27 =2x- 2 7 Title xloll yll 解

想請問第（2）小題和第（5）小題怎麼解？有關機率的問題

頁 第 3 共 5 | Twith 數學甲 百 345 2 5. 數學課老師用取球方式進行遊戲,由同學從装有相同材質的紅球 ml 顆與白球n顆(m,n皆 為正整數)的不透明箱中取球,規定「每局」為連續取球兩次,每次取出一球記錄顏色後放 回箱中(每次取球結果互相獨立且每一球被取出的機率相等)。每一位同學玩遊戲最多三局, 過程中,若某局取出兩球為同色球即「失敗」且結束該次遊戲換下一位同學;若連續三局 取出相異色球,則此同學遊戲「成功 請選出正確的選項。 1當m=2,n=3時,玩一次遊戲成功的機率為 cici ? % 2x3 2 6 5 7 50, 66 - 25 to 3 3 syg 2*7 (2不論箱中裝有多少顆球,一次遊戲成功的機率不大於- 8 (3)當 | ml-n|(紅白球數差距)越大,玩一次遊戲成功的機率越小 (onin) 12,15. (412) 444 - 7 760 (4)當m=n時,連續 60 位同學玩遊戲全都失敗的機率為 - (5)可以找到適當的(int, n),讓連續玩遊戲 60 次全都失敗機率大於 2180 u)