求解這兩題🙏🏻

【例13】 設 x ∈R,試解方程式 [3x]+2[x]-5=0. 5 # 07;5<3x<6.35 <x<2 10<x<1 (3x)+2(x) = 5 2 3 5353x24 3 44 5 > 457x<5 183252 Sol11 【例14】設x∈R,試解方程式x²-x-[x]=0 n (3-2-1 €2 2 x= x < x < x = x+1. 54= x² = 2x50 Ly = x² = 2 x +1 70 LY 練習 23<3 0<X<\ or \<x<? 470 。 2 4<0 (x)=0. f of 470 x=00X (10) <0 @ 1= x²-x x²-x-1=C 21X-2 [2]=22 Salz: floor function 12~3 1.設x∈Z且滿足x=4,則滿足條件的x共有幾個?

求這三題的過程 謝謝！

L000 In exercises 37-39, determine values of a and b that make the given function continuous. zeros at f(x) #C Some nu Theorer 2 sin x if x < 0 unction continu- X nction should be 37. f(x)= a if x=0 bcosx if x>0 52. For fo Does t

第六題 第二個問題怎麼解

6. Let f(x) = ln(3 – In x). Find the domain of f = (0, ey) and its inverse function f-1(x) = e(3-e“). logg C dx 1 7. Evaluate 1. O

求救第55題 完全看不懂他要我幹嘛

Year slenue Req) = 1932 1958 +1000 q R 9)=-1000q =74 1963 1968 COM If the price in dollars of a stereo system is given by 1000 p(q) + 1000, 1000 ² q where q represents the demand for the product, find the mar- ginal revenue when the demand is 10. 54. Profit Suppose that for the situation in Exercise 53 the cost in dollars of producing a stereo systems is given by C(q) = 0.2q2 + 69 + 50. Find the marginal profit when the demand is 10. 59. Marginal Product of Labor The output y of a manufacturing y process is a function of the size of the labor force n using the function 1990 +1000 1971 1974 = 990 197 197 19 19 1 y = kVn. The marginal product of labor, defined as dy/dn, measures the rate that output increases with the size of the labor force, and is a measure of labor productivity. (a) Show that (c) Using the a cubic f respond the rate and 200 (d) Discus descri part ( the y (e) Exp data calc ful x C(x) = 58. Money 1955-7 dy k dn an (b) How can you tell from your answer to part (a) that as the size of the labor force increases, the marginal product of labor gets smaller? This is a phenomenon known as the law of diminishing returns, discussed more in the next chapter. 56. Profit An analyst has found that a company's costs and rev- enues in dollars for a product are given by x2 C and R(x) 2x 2 5000' respectively, where x is the number of items produced. (a) Find the marginal cost function. (b) Find the marginal revenue function. (c) Using the fact that profit is the difference between revenue and costs, find the marginal profit function. (d) What value of x makes the marginal profit equal O? (e) Find the profit when the marginal profit is 0. (As we shall see in the next chapter, this process is used to find marimum profit.) A wher in bi find year (a) (C) (e) nad since

51最後怎麼算？sec c算出來後 我就看不懂要怎麼弄出c的值了

Value Using the Mean Integrals In Exercises 47-52, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. 47. f(x) = x3, [0, 3] [3 19 [0, 6] 4' = 48. f(x) = (x, [4,9] 50. f(x) = [1, 3] , 3] 9 - x2 49. y = , r3 - T [15 TT = 51. f(x) = 2 sec? x, 52. f(x) = cos x, 3' 3 4² 4

第四題我不知道為什麼選F 懇求各位大大的幫助

(A) familiar (B) honor (C) device (D) removable y(E) known as (F) protest (G) symbol (H) twisted into (I) associated with (J) historical 910022 Virgid 916 Yad Because of Vaaler, the paperclip played an important 2. 2 role in Norway. During World War II, Norway was occupied by the Nazis. Norwegians were prohibited from Pracanica by the Nazis Norway wearing any 3. of their national unity, such as buttons with the initials of their king. Thus, in 4. , they started wearing paperclips to show their solidarity. The reason for doing this was simple: Paperclips were a Norwegian invention whose original function was to bind together V og to anoise guinis (0) 2. q 3. 4. . el 【104 學測】(題號37-39) () (L A V

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

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).