第46題 一直不是很確定😅🥺🥺

54. Differentiability and Continuity on an Interval Each figure in Exercises 43–48 shows the graph of a function over a closed interval D. At what domain points does the function appear to be a. differentiable? b. continuous but not differentiable? c. neither continuous nor differentiable? 55 5 Give reasons for your answers. 44. y 43. y = f(x) y D: -3 = x < 2 2t y = f(x) D: -2 < x < 3 2. 1 1H -3 X X -3 -2 -1 0 1 2 -2 -1 - 1 2 3 10 -1 -1 - 27 -27 45. (46. y y y = f(x) D: -3 < x < 3 y = f(x) D: -2<x<3 3 RE w 1 -3-2-10 -1 X -2日 2 1 2 2 -2 -1 01 1 3

請問這三小題要怎麼寫⊙﹏⊙

64. Let f be a function that is differentiable at x = c. noa. Explain why f(x) – f(c) f'(c) = lim X - C - X->C

請問第21跟23題怎麼算？

erlei 35 Range + 10. x - xy + y + 1 = U x 2 3 4 x + 3 3 2 + Finding the Domain and Range of a Function In Exercises 17-24, find the domain and range of the function. Use a graphing utility to verify your results. See Example 2. - . r = bylo No = > - = - X 1 = - X 1 2 - = = -1 – > 18. f(x) = 5x3 + 6x2 – 1 17. f(x) = - x2 – 2x + 3 lxl Domain: (0o,0) 0 (0,00) 19. f(x) = 20. f(x) Ranga : y=-/or Zo: 1 X – 9 (x - 5, x 20 V 21. f(x) = 3x + 2, x < 0 22. f(x) = (3x – 5, x < 0 2 - x, x 20 23. f(x) = X – 2 x2 x + 4 Domain : (-00,oo 1 Domain :(to ,-4) U(-4,00) Rango: (+60, 120 (1,00) = = 24. f(x) x4 V x Range: (-os, as)

不好意思想問題目是什麼意思，如果是畫圖找切線為什麼會給兩個x值，想知道第一題怎麼寫，附答案

Exercises 2.7 Answers to selected odd-numbered problems begin on pa Fundamentals In Problems 1-6, sketch the graph of the function and the tan- gent line at the given point. Find the slope of the secant line through the points that correspond to the indicated values of x. 1. f(x) = -x2 + 9, (2, 5); x = 2, x = 2.5 ( 2,5= =

請問第五題怎麼算？ 謝謝

(xp y (x2, y2) Finding the Slope of a Tangent Line Exercises 3–5, find the slope of the tangent line the graph of the function at the given point. 4. f(x) = 2x2 – 3, (2, 5) 3. f(x) = 3 – 5x, (-1,8) 5. h(t) = 12 + 4t, (1,5) Finding the Derivative by the Limit Process I Exercises 6–10, find the derivative of the function by the li process.

求解：9、17、27,謝謝~

Ad-numbered problems begin on page ANS-8. limbinht lim or state that it does not tolista O 1 . 7. lim 8. li 10 t sect csc 4t to 2 sint lim -4.1=4, 10. 170 t cost 31 sin26t 11. lim lim .36 12. t->0 t2 to 36t² sin(-41) sintt t 1 + sinx m +01 + COS X -36 # sin(x - 1) 13. lim x=1 2x - 2 14. tang n = 0 3x is sin(x-1) 2(x-1) - IN 们

混合題第31題，它的題目什麼意思？ 求解🙇🙇，萬分感謝☺🙂

EL 35. 這位老師很生氣,Hugo 沒勞化 36. 雖然這塊牛排看起來像塊岩石 Dear Ms. Louise, Today was my precious little girl's first day in high school. She was thrilled that she would finally meet her new classmates. But when she woke up, she found that she had a big red pimple on her nose! She worried about it so much that she told me she didn't want to go to school. I knew that she felt embarrassed about having a big red zit on her face, especially when she was about to meet new friends and wanted to leave a good impression on them. However, as a mother, I just couldn't let her skip the first day of school. So, I made her go to school this morning. Did I do the right thing? Worried Mother Dear Worried Mother, I think you made the correct decision. Though her concern of making a bad impression on her new friends is understandable, she needs to learn that most people focus only on their own problems and don't even notice others'. Her friends would probably not notice her pimple at all. I think she will gradually figure this out. Don't worry. Talk to her as usual. She must have plenty of exciting stories about her new friends to share with you tonight. Ms. Louise ) 29. What does Ms. Louise do? (3%) A (A) She is a column writer who gives advice and suggestions. (B) She is a school nurse who helps keep children healthy. (C) She is a company manager who is in charge of a large group of workers, (D) She is a family doctor who takes care of people and treats their diseases. (B) 30. How would you describe Worried Mother and Ms. Louise? (4%) (A) Angry; calm (B) Guilty; comforting. (C) Embarrassed; proud. (D) Understanding; confused. 31. In Ms. Louise's reply, the word others' refer to others' (4%)

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

求解第2.4.8題 謝謝！

finally 14. 全新試題 the structure collapsed. With only was at this moment that all of them suddenly became very to build the tallest structure. Just before time ran out, they successfully built inches high, winning the challenge. Thanks to this experience, Scott and his teammates finally came to understand the true spirit of teamwork. (D) had been (A) 5. (A) In order B 16. (A) constru co 7. (A) Still a ( 08. (A) since (B) 9. (A) mate ) 10. (A) (A) has been get (A) 10 AD B) 2. (A) encouraged C) 3. (A) to B) 4. (A) stable D) 5. (A) From B)6. (A) plans i CS 7. (A) what Dx8. ) (A) Unfortunately 9. (A) mention C10. (A) look after (C) is being (C) encourages (C) as (C) enjoyable (C) Into (C) to plan (C) who (C) Normally (C) achieve (C) figure out (B) will be (B) encouraging (B) of (B) capable (B) Among (B) planning (B) which (B) Especially (B) promise (B) call for IV. 文意選填 ※第一篇 (D) encourage (D) for (D) probable (D) With (D) planned (D) when (D) Slightly (D) adjust (D) run into (A) whereas (F) conduct Every that prescrit features of Rules members ※第四篇 1. Hi, my name is Tom Wujec. Let me introduce myself first. I was born in Canada, and I from the University of Toronto with degrees in astronomy and psychology. Chances are you don't know me, but I guess you probably have heard of the Marshmallow Challenge 2. was created by me. Since its invention, it 3. around the world by people from all walks of life. 4. my surprise, it has produced some unexpected results. 5. better understand the results and their though, th Rul in the M implications, I conducted a study and got some interesting findings. One of them was that the average a tape,

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).