微積分

D (2) f(x) f(x) 2 x² (x²1)4 √2x+1 x²-1 (~2x) (3x²+1) (x²1)5 3x²+2x+1 2x+1 (+²= 1)²

請問這題怎麼解🙏🙏

15) J Hit dx VX+1 + 5X

第一行是怎麼變第二行的 求解

+ 。 +4y=cos 2x y- ancoszx+Ctinet +cosrx +4 29 may 14. 團隊專題方法之比較、聲明 只要可行,就應使用特定數迷,因爲它 * +9y = csc 3x 較為簡單。就以下問題,以參數變異法與 y" – xy' – 3y = x2 其做比較。 41' + 5y = e2x csc x Yp=-cosex Sineklarat dx + sinax Scorex dx s z yen 合 & cosex + 2xsinux truh (X) ruft cash CPMSG-=(x)dh dx

統計學 第35題 請問裡面的e代表什麼意思？ 第二小題的0.423怎麼來的？

試問 (3) E(X) 0 )XCa -10 fi -2.5 02-7-6--0,08 課。小考共有 象在測驗時必 -0,5 e .0.5 P{X:0) - * o - l = 0,60)# 其中只有一 要準差。 0次,並以 表抽出之 1.國國際機場旅客到達行李託運站服從卜瓦松分配,每分鐘到達 10久,試求: (1)1分鐘內沒有旅客到達之機率。(2) P(X=()。 15秒內至少有1位旅客到達之機率 。A_X] 公司的電話總機在忙碌時刻,平均每分鐘處理了通電話,又該總機每分鐘最多可接通: 0.18 5通電話,試以下瓦松分配求算在某分鐘內,該總機負擔過重的機率為何? 3. 佳佳化學工業公司每個月發生廢棄燃料意外起火事件之次數為0.1次,試求一年中發生 1件意外事件之機率為何? 4.設台北貓空纜車根據過去資料顯示,平均每半年發生無預警停駛3次,假定無預警停駛 ) 次數呈一下瓦松分配,試求: (1) 下一個月台北貓空纜車沒有發生無預警停駛的機率。 (2)下一個月台北貓空纜車至少發生1次無預警停駛的機率。 ' p(X21) - - p[X=0) 35. 設一工廠所製造玻璃每100平方呎有一個氣泡瑕疵,今購買該工廠生產的一片10呎寬、 1 -0,60%= 0.393* 30呎長的玻璃,試求: 0! = 0,05 # (1)沒有氣泡瑕疵的機率。 p(X=2)= e: (2) 恰有2個氣泡瑕疵的機率。 = P(X=2) - P(X1) 36. 設隨機變數 Z的分配為標準常態,試求: 01423-0199 (1) P(Z <0.5) (2) P(Z > -1.28)。 (3) P(-0.7 <Z< 3.1)。 (4) P(12] > 1.5)。 17 外遊變數 Z的分配為標準常態,試求下列值: 11. px-D) - -3 > e o 恰P=y1.4。 - 房間, 昌平均 - 0.2分 o ? 的限 能準

可以問第二題第三題嗎 第二題的du的根號x前面的2跟分子的1怎麼來的 第三題的du怎麼來的 🙏

00:20 ...l 4G drive.google.com PDF 4-2.pdf 登入 隨堂練習參考解答 基本題 1 (1) 5 63+2 dx (2) 1V5 * die 3t dx (3) STP dt (5x ſi Sol: (1) u = 5x + 2 · du = 5 dx 1 ut 5 1 -1 u ,-3 5 3 +C (5x + 15 1 listt.2jdx = du = 5; - -(5x + 2) (2) u = Vx-1 · du = (-1) dx = 5+27x du = 2 .(V5-1" + tư (x-1)* , U= - dx 2x = +C Vx 4 2 (3) u=ť +1 · du = 2t dt u 3t dt = Vt? +1 do = 2 du = Ju du = -2 Ju=3+1+C 3t 1 ſu 21 - 2 進階題 Find [f"(x)dx if f(x)=xVx? +1 Sol: d dx 頁次: 1 | 1 5.6"(x)dx = S. S)dx= ["@+C f'(x) = Vx3 +12 + 3.13 + SO K 12 ...

第十題求解題過程，感謝🙏

where ci n n Writing a Limit as a Definite Integral In Exercises 7–10, write the limit as a definite integral on the given interval, is any point in the ith subinterval. 7. lim § (30; + 10) Ax; 3c 8. lim Ë Vc? + 4 Ax; [-1,5] [O, 3] 9. lim Š 10. lim § (2-4 sin c;) Ax; [1, 5] [0, 1] A»0 n n 3 1 + Ax; 141-0 ||A||→0 i=1

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

Z (b) Use the acceleration curve from par (a) to estimate the 10 seconds. What are the units for jerk? 45) The lel defined ||||| V has a vertical tangent line at (0,0). and jerk at = 38, Let f(x) = V. x ( (a) If a 40. use Equation 2.1.5 to find s'a). (b) Show that f'(o) does not exist. (c) Show that y- (Recall the shape of the graph of f. See Figure 1.2.13.) 39. (a) If g(x) = x?, show that g'(0) does not exist. (b) Ifa * 0, find g'(a). (c) Show that y = x2 has a vertical tangent line at (0,0). c (d) Illustrate part (c) by graphing y - x2) if the sided (a) F | 40. Show that the function f(x) = |x - 6 is not differentiable at 6. Find a formula for and sketch its graph. (b) Where is the greatest integer function () = [x] not

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

這題怎麼解？

yo-1 5. lim 1-1 X – 1 =?

想請問這題如何解（統計學，計量經濟學）

已 - 1 - - - 2. 令 y = 2. KWW-3.educ,則T =? var(x)=? 進行假設檢定IH-、=30,檢定統計量to=? - - X Simple Statistics: mean IQ KWW 101. 28235 35. 74439 educ 13. 46845 n=935 expert 11.563648 I .........18.1.17...1..16. IQ KWW educ exper IQ 226. 5819 47.5476 17. 0517 -14.8103 Covariance Matrix KWW educ expert 47.5476 17.0517 -14.81034 58. 3511 6.5128 0.5832 6. 5128 4. 8253 -4. 3778 - 0.5832 -4. 3778 19. 1370