微積分

2 -A 微積分練習題 110.12.28 1. 試用微分的方法求 的近似值(以分數表示) 26.98 2. 將水注入右圖圓錐體容器中(圓錐形體積= 'hir 為h之1/3),水上升的速 度為3公分/秒,當水深為6公分時,其水量的變化率為何? 3. 求f(x)=2-3x--x之臨界值,增、減函數之區間,反曲點,並判斷其相對極大 或極小值,最後並繪出其圖形? 4. 判斷下列函數之增減函數的區間。 r'+4 (1) f(x)= (2) f(x) = 4x -x? 2x + 3 5. 一個底部為長方形的木箱(長為寬的2倍),體積為180m,其材料成本如 下,底部每m 為15元,箱頂蓋子每m'為10元,四周每m'為5元,求在總 成本最小下,箱子的長、寬、高應各為多少? 6.某廠商之需求函數為 D(x) = 100 -0.0lr,求(a)p=40之需求彈性(b)廠商最大收 益之生產量(c)若廠商想漲價5元,其總收益會增加還是減少? 7. 某馬戲團依據過去的資料知道若票價為200 元,則平均會有1000名觀眾進 場,若票價每增加10元將會流失 100名觀眾(每減少10 元會增加100 名觀 眾),此外,觀眾在戲團內平均會花費20元購買飲料或零食,請為該馬戲團決 定,在總收益為最大的情況下票價應為多少? 8.某廠商之需求函數為 D(x) = 1000 -0.02x,求(a) p=600 之需求彈性(b)廠商最大 收益之生產量(c)若原P=600 元,廠商想漲價30元,則其總收益會增加還是減 少? 9.台灣人口若屬於指數型成長,假設 2000年台灣人口數為2200 萬,2010 年人口數為2300 萬,請預測 2015 年台灣人口數約為多少(算至萬位數)? 10. 某種化學肥料於施作後,測量其單位面積土壤中的含量為100ppm,經過 5天後其含量減至80ppm,若天氣條件不變的情況下,請問經過20天後其 含量減至多少(算至整數)? 11. 解下列x(小數點第2位後四捨五入) (1) 4e4x = 14 (2) 2 + 4e in 4x = 8 (3) 4 In r2 = 16 12. f(x) = 3x-2x+1 求在re-13]時滿足 mean value theorem 時之C值。 不安全 - Ims.ntpu.edu.tw

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 ...

大一普化5.58求解

/r'277e777y 記 的 B 9 5.61 A mixture of gases contains CH4, Co2Heo, and CHS. the total pressure 1s 1.50 atm and the numbers of moles of the gases present are 0.31 mole for CHu, 0.25 mole for CH日c, and 0.29 mole for C3Hs, calcu- ]ate the partial presSures of the gases. A 2.5-L fask at 15”C contains a miXture of three gaseS, N2, He, and Ne, at partial preSSureS of 0.32 atm for N2, 0.15 atm for He, and 0.42 atm for Ne. (a) Cal- culate the total pressure of the miXxture. (b) Calculate 出e volume in liters at STP occupied by He and Ne 議 the N2 1s removed Selectlvely. NN Dry air near sea level has the following composition by volume: N2, 78.08 percent; O,, 20.94 percent; Ar, 0.93 percent; CO,, 0.05 percent. The atmospheric pressure is 1.00 atm. Calculate (a) the partlal pres- Sure of each gas in atm and (b) the COohcentratlion Of each gas in moles per liter at 0。C. (7/7///- Because Volume is proportional to the huber of moljes Present, mole fractions of gases can be eXpresSed as ITatios of volumes at the same temperature and preSSure.) A mixture of ITmHg. If the partial pres- mmHeg, what is the partial pres- QT pressure of water at 285C 三 Sure of helium is 368 erature. (1) Whiceh container has the smallest mole Shi 人

大一普化5.50求解

3.43 AN 失 交 (方 N 全 只 憲 5.49 5,@ Re Problems 5 0t ln the stratosphere itadiation from the sun. and presSsure of ozone in Ths absSQTt Typieal the Stratosi Kandl0人10 am re spectively. How many ozone molecules are present in ]l.OL ofair under these conditions? Assuming that air contalns 78 percent N2, 21 pereemt O>, and 1 percent Ar, all by volume, how many mol- ecules of each type of gas are presentin 1.0Lotair 肚STP? A 2.10-L vessel contains 4.65 g ofa gas at 1.00 atm and 27.0。C. (a) Calculate the density of the gas In grams perliter. (b) What is the molar mass of the gas。 Calculate the density of hydrogen bromide (HBr) gas in grams per liter at 733 mmHg and 467C. A _ certain anesthetic contains 64.9 percent Co, 13.5 percent H, and 21.6 percent QO by masS. At 1205C and 750 mmHg, 1.00 L of the gaseous com- pound weighs 2.30 g. What is the molecular formula 9f 人he compound? Aecompound has the empirical formula SF4. At 20.0 0.100 g of the gaseous compound oceuplesa Volume of22.1 mL and exerts apresSure of 1.02 atm, What 1S its molecular formula? Dissolving 3.00 g of an impure Sample 0f calcium carbonate in hydrochloric acid produced 0.656L 人 carbon dioxide (measured at20.0C and 792 mmHg). Calculate the percent by mass of caleium carbonate in the sample. State any assumptilons, oleulafe the 和ass in orams Ofhydrogen chloride bro-

大一普化 5.36求解

5.38 9389 信4 5,42 sphere (about 30 Where the temperatu lbove the surface of Earth), >and presSure are 一235C : h gd 交 and 3.00 XX 10 atm, respectively. Calculate the final Volume of the balloon. The temperature ot 2.5 L of a gas initially at SUN increased to 2507”C at constant volume. Calculate the final pressure of the gas in atm. The pressure of 6.0 L of an ideal gas in aflexible contalner 1S decreased to one-third of its original presSure, and 1ts absolute temperature 1s decreased by one-half. What 1s the flnal volume of the gas? A gas evolved during the tfermentation of glucose (wine making) has a volume of 0.78 L when mea- sured at 20.1?C and 1.00 atm. What was the volume of this gas at the fermentation temperature of 36.5 C and 1.00 atm presSure? An ideal gas originally at 0.85 atm and 66”C was allowed to expand until its final Volume, preSSure, and temperature were 94 mL, 0.60 atm, and 45 C, respectively. What was its initial volume? The volume of a gas at STP is 488 mL. Calculate 1ts volume at 22.5 atm and 1507C. A gas at 772 mmHg and 35.0”C Qceuples a Volume of 6.85工. Calculate its volume at STEP. Dry ice is solid carbon dioxide. A 0.050-g sample ot dry ice js placed in an evacuated 4.6-L vessel at 30。C. Caleulate the pressure inside the VesSel after all the dry ice has been conVerted to CO gasS, Avolume of 0.280Lofagas at STP weighs 0.400 g. Calculate the molar mass Of the gas. Aquantity of gas Weighing 7.10g at741tor and 445C oeeupies a volume of 5.40L. What is its molar mass? Si人2 5.93 5.54 Dalt 和Ae0U76 5 5.56

請問有人會第三部分嗎謝謝🙏

7 practical abilities: cl 尼 (LSIKLs 和 Match 1-8toa-htomake sentences7 人 SQ 1 Isalwaysqificult to allocate ag_ 卻志 2 You need to learn how to delegate 3 Ma二 like about my boss is she always lets me Set ck_ We're falling @ ILs difficult to stay within AA If wecontinue like this, we should meet 二廬 Hi, Melinda, it's Hanna, Ineed to getan Tm sure wedl be able to catch 襯_ Hedte司 六 b behind schedule, so we all need to work this weekend- update on how the project is progressimg,。 ~d_tasks-you cantpossibly do everything yourself, e up-there are three more weeks left。 f on with my workonmyowm. 潑 budget-wealways overspend- ~h thedeadline without too much trouble, %@swWuonem 3 Complete the email with the correctform of'words from 2. Dear Jan, jm afraid 上looks 由8 we are not going'to be able to meet the next Friday. We've fallen behind 2cjauue_ because we were not 3 SUffiGiG We need more 5 汪記 with ee appropriate'skills to be put on 了he DrGJeGt immediately. Of course, 了his does meanm 也at we wont be able to stay 了 our6_____either WilISSIIVOU # after our team meeting tnlS afternoon to let you know what iS deeiqledl- Very best wishes, Graham Lud 有

請問有人會第二部分嗎謝謝🙏

3 | Practice file Working with words IT PutftheIetters im brackets in the correctorder to make words thatmatch the definitions. 1 something available to exPploit and use: yesolerces- (ESCRORUSE) Sweulg_(csEHDLUE) 2 ftimetable of activities: 3 news onhow something is progressing: (UTEPAD) 4 money spending plan: bpe (BDTUGE) 5 thelast day for finishing a piece of work or projeetk NWZ/ (ADENDEL 6 working together: 0(EAWKTMRO) 7 practicalabilities:_<erlUe_(LSIKLS) 2 Match 1-8 to a-h to make sentenees7 SO 1 Itsalways difficult to allocate 4 炙訕 2 youneed to learn how to delegate 3 由 about my boss is she always lets me get 4 Were falling 1 5 Isdifficult to stay withim 人 6 HIfwecontinue like this, weshould meet 7 Hi Melinda, is Hanna,Ineed to getan 8 Tm sure we beable to catch 襯- p pehind schedule, so we all need to work tfhis weekend. update on how the project is progressing, ~d_tasks-you cantpossibly do everything yourself, \ 印- there are three more weeks left. f onwith my workonmyowrm 痊 budget-wealways overspend- ”h thedeadline without too much trouble, 3 Complete the email with the correct form OfWords from 2.