求解...

the race. point (0, 2), find f(4) and f'(4). I 37 19. Sketch the graph of a function f for which f(0) = 0, f'(0) = 3, f'(1) = 0, and f'(2) = -1. . nners the - = = -

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

(d) Use the definition of derivative to prove that your guess in part (c) is correct. 14-21 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. 14. f(x) = 3x - 8 15) f(x) = mx + b 16. f(x) - 4 + 8x - 5x? (17) f(x) = x - 3x + 5 18. f(x) - x + V g(x) - 19- x? - 1 20. f(x) 21s(x) x2 2.x - 3 (hours) arger. The graph hat the battery purs). (r)? graph - a 22.) a) Sketch the graph of f(x) - V6 - x by starting with the graph of y # and using the transformations of Section 1.3. (b) Use the graph from part (a) to sketch the graph of f! (c) Use the definition of a derivative to find f'(x). What are the domains of f and f'? (d) Use a graphing device to graph f' and compare with your sketch in part (b). lo-TE 23. (a) If f(x) = x + 1/x, find f'(x). (b) Check to see that your answer to part (a) is reasonable by JE comparing the graphs of f and f'. 1 (hours) shows how 24. The table given tho hai

想請教各位，這篇文章是否有文法或單字上的錯誤，感謝糾正 Volunteers activities about caring for the elderly. The school arranges students to go to the nursing center ... 繼續閱讀

求解e f

-3 29. [Maximum mark: 24] [without GDC) The function f is given by f(x) = 2x+1, xeR, X+3. (a) (0) Show that y=2 is an asymptote of the graph of y=f(x). (ii) Find the vertical asymptote of the graph. (ii) Write down the coordinates of the point P at which the asymptotes intersect. (b) Find the points of intersection of the graph and the axes. (c) Hence sketch the graph of y = f(x), showing the asymptotes by dotted lines. (d) Show that f'(x) = -7 and hence find the equation of the tangent at (x-3) the point S where r=4. [4] [4] [4] [6] (e) The tangent at the point T on the graph is parallel to the tangent at S. Find the coordinates of T. (6) Show that P is the midpoint of (ST). 1 ] [5] [1] MacD

第六題，怎麼算

6. Suppose that the targent line to the graph of a function f at x = 1 passes through the point (4,9) = and that f(1) = 3. Then f'(1) = 2 JJ斗笠 、恐日頭(60 分)

求解28題 感恩🙇

36. Sup ang 22-25 Explain, using Theorems 4, 5. 7. and 9. why the function is continuous at every number in its domain. State the domain. 2.x2 - x - 1 2 22. F(x) 23. 20) = r2 + 1 By Le (a) (b 24. h(x) = cos(1 – x?) 25. M = N DI 38. W tir 26-29 Use continuity to evaluate the limit. 26. lim x 20 – x2 27. lim sin(x + sin x) ULTET (28) lim x'tan r 11/4 29. lim x®/Vx2 + x - 2 IX 30. Show that f is continuous on (-00, ). 39. S f(x) = x2 if x < 1 x-1 if x>1 31-32 Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the whı sont o LINE TERANG 1633 是

求解第33題 感謝🙇

30. lim x csex 21 29. lim sec ---(4/2)+ x x 22 31. lim x==2 4x + 4 32. lim X-2+ x x² - 2x - 8 x² - 5x + 6 8 33. Find the vertical asymptotes of the function x? + 1 3x - 2.x2 1 ||||| 1 34. Determine lim and lim X-TX r- (a) by evaluating f(x) = 1/(x - 1) for values of x that ap- proach 1 from the left and from the right, (b) by reasoning as in Example 8. 35. (a) Evaluate the function f(x) = x2 - (24/1000) for x = 1.

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

請問為何第五題的答案為due to? 其他選項as a result of , supposed to 為何都不能選？ 謝謝你們

Part B 4 The 1 of UFOs (Unidentified Flying Objects) is a source of controversy that often 2 people into two separate groups: those who believe that UFOs are the spaceships of intelligent 3 from other planets, and those who and believe these sightings 5 have some other explanation. Those in the second group say these sightings could be the effects of a distant planet, a weather 6 or airplane lights, for example. Another possible explanation is that the people who report the sightings could be imagining what they 2