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

請問第31題要怎麼看？謝謝！

lesses, secrets, and vulnerabilities No: S. ng I grew my spine and took back the life 2 t= 002 A B 7 31. 在O點依序水平拋出三個物體,如圖所示,假設三物體的初速度分別為 1、吃、吃,且落地時間分別為1、t、t,下列敘述正確者為? (A) VA > VB > Vc ; ta > tp >to (B) v = Vn = vc i la = 13 Etc (C)VA < VB <Vc ; ta > tp >to (Dr. <3 <ve it <lg<te (E) VA <3 <vc i to <l <te 【雄中模考) 32. 如圖,一條小船位於 200m 宽的河正中央4點,在距4點10003m 岸邊 的下游處有一危險水域。假設4處水流都保持4m/s方向平行於 - 100V3 m 危險水域 岸邊,為了使小船能避開危險區而成功登岸,則小船對水的速度 A 至少需為多少m/s? (雄中模考) 岸邊 413 (A) 2 8.3 (B) (C) (D) 4 (E) 8 3 3 U <o Texcol - 33. 某物體運動時,其位置與時間的函數為X=3+t-2,則物體於下列時間何者可能往-x方向 m

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

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

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

想問b為什麼在3時不連續 ？ 我的想法是：在3時存在，而存在一定連續。

45. Let --X V = if x < 0 f(x) = 3 - x = 3- x if 0 < x < 3 (x - 3)2 if x > 3 - xo+ xo- x>0 (a) Evaluate each limit, if it exists. (i) lim f(x) 3 (ii) lim f(x)0 (iii) lim f(x) fxO Flatte (iv) lim f(x) O (v) lim f(x) 0 (vi) lim f(x) 0 ( (b) Where is f discontinuous? at 0 and 3* o 3 (c) Sketch the graph of f. tis- x x x 3

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= =

請問一下這題怎麼算😭好難

Vout - 5 volt D2 +5 vol o Vout D OVORI = Vout == 4.310 v ok suming the diodes are | (b) tions shown in Figure P9.23 D -9.3 大 li (c) WO Do V 12 +7 V o bin 88. I won T08 . 9.24 Sketch the output waveform and the voltage transfer characteristic for the circuit of Figure P9.24. Assume an ideal diode, us (t) = & sin (it), V, = XV, Ri = 812, and R2 = $ 12. 10 4 lo lo mm ogiloc www bools boRi t V. -Vo 15 k12 15 k92 1 vs borbo R2 V 4V V c) (d) bagnozib Figure P9.24 OU 29,22, find the range of Vin 25 Repeat Problem 9.24, using the offset diode model

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31題 謝謝🥺

USC c) in (C) at first terminal (D) illness (E) frailer (H) difference (I) from (J) confined The doctors had some bad news for Jo Bloomer. Her second child, Lola, had a very rare 21. condition known as A-T. 22. she couldn't accept the fact that her family was so unlucky. A-T is so uncommon that, at the time, only sixty children in the UK suffered 23. it. Three-year-old Lola's condition meant she would gradually grow 24. She would then start to develop more and more disabilities*. Most A-T sufferers are 25. to a wheelchair by the age of ten. Eventually, she would die from this strange 26. __, probably in her early twenties. Luckily for Lola, her mother 27. to simply sit around and wait for her daughter to grow weaker and then die. Life, 28. was just too precious. Instead, she wanted to do something special for her. She wanted to make a significant 29. in her life. All this led Jo to make a promise. Holding her daughter 30. her arms, she vowed* to take her to each of the Seven Wonders of the World before she died. She was going to help little Lola live her short life to the full! 註:disability 缺陷;障礙 Vow 立誓 U I 21. 22. J . 23. 24. 25. 26. 27. 28. 29. 30. . I GE EG IV. 閱讀測驗:9% The movie Patch Adams was released in 1998. Based on the life of Dr. Hunter "Patch” Adams, it tells the story of a man who firmly believes laughter to be the best medicine. The famous comic actor Robin Williams plays the lead role. His wonderful portrayal of the doctor's quest* to relieve as much suffering as possible led the film to be nominated* for several awards.