（大一微積分） 請問這題這樣寫正確嗎？背流程寫的😅，圖一為需用到的定義 正確的話，想問紅色圈圈的1是怎麼來的？

DEFINITION Let f be a function defined on some open interval that con- tains the number a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a is L, and we write lim f(x) = L x→a if for every number &> 0 there is a corresponding number 8 >0 such that | ƒ(x) − L| < ɛ if 0 < x-a <8 then

我想請問 原本fn只在所有compacts上一致收斂 D裡面會不會也包含沒辦法closed and bounded的部分 但我最後要證明的卻是在整個D上f都連續 這樣①③的選擇會不會只證明f在D中的任何compacts連續呢 如果會的話要怎麼改善證明 （高微證明小白求解..

Question 2 [10] Let {fn (2)} be a sequence of continuous complex functions defined on D C C and f(z) be a complex function defined on D. Prove by e-N definition that if fn(z) converges uniformly to f(z) on compacts in D, then the limiting function f is also continuous. 0₁0. fn 3 f for z For every Z in K E > = N(6) € ₁ s.t. Unz N₁ | fn (2) - f(z)] < 1/10 N= . in any compact sets K≤p. @fn 75 20, 2 820 sit.lzx]<8>lfe)-f(x)]<- continuons for z in D. For every z, & in D. VE>O, we choose the above N and f if Iz-*|< 8, then s.t | f(2)= f(a)| = |f₁z) - fn(z) + tn (2) - fn(x) + fn(x) – frasl ≤ | fn(z) - f1z)| + | fn(²2) - fn(x) |+| fricas) _flox) | = D E 1/4 + 1/3+1/²/3 = 3 =.E.

請問大一統計學這兩題有人看得懂嗎🥲

2. To study the attitude of mother and father towards their daughter participating in the outdoor games, a sample of 200 fathers and 250 mothers was investigated. In these two samples, 120 fathers and 50 mothers preferred their daughter to go for outdoor activities. Can it be concluded at a=0.01 level of significance that the proportion of father is significantly higher than that of mother in preferring their daughters for outdoor activities? 3. A firm has a generous but rather complicated policy concerning end-of-year bonuses for its lower-level managerial personnel. The policy's key factor is a subjective judgment of "contribution to corporate goals." A personnel officer took samples of 24 female and 36 male managers to see whether there was any difference in bonuses, expressed as a percentage of yearly salary. The data are listed here: Gender Bonus Percentage Female 9.2, 7.7, 11.9, 6.2, 9.0, 8.4, 6.9, 7.6, 7.4, 8.0, 9.9, 6.7, 8.4, 9.3, 9.1, 8.7, 9.2, 9.1, 8.4, 9.6, 7.7, 9.0, 9.0, 8.4 10.4, 8.9, 11.7, 12.0, 8.7, 9.4, 9.8, 9.0, 9.2, 9.7, 9.1, 8.8, 7.9, 9.9, 10.0, 10.1, 9.0, 11.4, 8.7, 9.6, 9.2, 9.7, 8.9, 9.2, 9.4, 9.7, 8.9, 9.3, 10.4, 11.9, 9.0, 12.0, 9.6, 9.2, 9.9, 9.0 (1) Is there significant evidence that the mean bonus percentage for males is larger than the mean bonus percentage for females? Use a a=0.05. (2) Estimate the difference in the mean bonus percentages for males and females using a 95% confidence interval. Male

想請教這一題微積分，謝謝！

2. (8%) Consider a real numbers and suppose that lim x→0√√x+s4-s² find s (there are two possible answers). = 3,

我想請問第二行算式中，為什麼平方之後，左邊會變成0？

Explanation: For all x = 0, 2π −1 < sin 0 < sin² X (²) 1 <1+ sin² ≤ 1, and < 1, so 2π X Therefore, lim For all x > 0, we have √ > 0, so we can multiply the inequality by √ without changing the inequalities. √ã ≤ √ē (1 + sin² Observe that lim x → 0+ +0←x ≤ 2. (²)) ≤2√x. √x = 0 and lim 2√√x = 0. x →0+ 2π √ē (1 + sin² ( ²7 ) ) = =0 X

請問有人知道這題怎麼求解嗎？🥺

= = Exercise 4.1.102: Suppose x" + 1x = 0 and x(0) = 1, x(1) = 1. Find all for which there is more , 1 than one solution. Also find the corresponding solutions (only for the eigenvalues).

統計～ 請問a.b小題要怎麼解🙏🙏

a. 4. The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour. Suppose the number of calls per hour follows a Poisson probability distribution. What is the probability that there will be less than one hour between 911 calls? b. What is the probability that there will be 30 minutes or more between 911 calls? c. What is the probability that there will be more than 5 minutes, but less than 20 minutes between 911 calls?

想請教這題的解法

3. Proof that there is only one intersect point between f(x) = 5x3 + 2x2 + 4x + 1 and g(x) = 2x2 + cos x. (Hint: use the mean value theorem) (10%) =

想請問學霸們畫線的地方是什麼意思？（看得懂英文，不過他想表達的我就不懂啦~QQ)-大一入門微積分

Precise meaning of limit x->a For each € > 0 there is a 8 >0 such that 0 <|x - al<8 = \|(x) – Ll<ɛ 1.Prove that lim (3x – 7)= 5 x 4 Prove : Preliminary Analysis : Let ε be any positive number. We must produce a 8 >0 such that 0<fx - 4<= |(3x - 7)- 51 < digital do consider the inequality on the right |(3x – 7)-5/<ε = 3x - 12/<€ 3(x-4)<ɛ how blu 4< = |- - 131x - 4 <E (x-4 < 2 3 domen. szondo otworo Now we see how to choose 8, namely, 8 = Of course, any smaller 8 would work Toolmo Formal Proof : Let & > 0 be given. Choose 8 = . Then 0 < x - 4 <& implies

數學/統計學/共變異數/相關係數 想請問一下題目上的第三題要如何求算ಥ_ಥ （網路上查到的題型都是實數對實數，這裡是給一個範圍⋯而且求的是開架跟天數而不是兩區的差別） 附上上課給的範例嗚嗚嗚 麻煩了ಥ_ಥ謝謝各位

Question 2 (125) V2 某家位於美國中部小鎮之小型房地產仲介,現想瞭解物件自委託到買賣成立所需的時間。該 公司分析近近三年來成交的 800 筆資料,整理如下表。 成交所需天數 30 天以內 31-90 天 90 天以上 總和 $150,000 以下 50 40 10 100 6 6:125 $150,000-$199,999 20 150 開價 80 250 0,3125 $200,000-$250,000 20 280 100 400 05 $250,000 以上 10 30 10 50 總和 100 500 200 800 如果該公司簽下委賣合約,開價在$150,000 以下,則成交天數在90 天以下的機率 為何? b. 如果事件 A表示成交所需天數在90天以上,事件B表示開價在$150,000 以下, 請問事件A與B 是否為獨立事件?試說明之。 C. 假設該公司將800 筆數據又細分為東區及西區(兩區房價分佈相似),並統計在售價 區間的平均銷售天數,其結果呈現如下表。試算共變異數及相關系數,說明開價與平 均銷售天數有甚麼關係。 平均銷售成所需天數 0,0625 a. 東區 西區 PC62 37 42 54 66 開價 $150,000 以下 $150,000-$199,999 $200,000-$250,000 $250,000 以上 71 82 46 50 出S(新) 法制度信天名之戈登发 才有哪 and AND cing 0 .action 2 (104)