請問兩個紅色問號的部分是怎麼來的🙏

131) 5. 1/2+1 100 ₁² lim (1 + =) * x →∞0 (1 + 1 = 2 ) * X // Y = 令y=(1+ In y = In ( 1 + 1 ) * = x In ( 1 + =) = 1 n ( 1 + + ) ? * =1 ? lim In y = lim X+∞ X-00 y=elny In (1+) → >> lim 1+*+-+*) 上 X-700 T lim y = lim elny = e' X-700 X-700 = e #

求解！謝謝！

Q 0-3. 若函數f(x) = x,則f'(x) 的定義域為 (1).(-1, ∞) (2).[-1,∞) (3)(0,0] (4).以上皆非

請問這題為什麼只能先對y積分？只是因為先對x的話積不出來嗎？

Evaluate the double integral: f(x, y) = ye; R is bounded by x=2 2 and y=0. ud hisborod【107 東吳巨資】 解:積分區域R如圖,只能先對 y 積分 s! Si yet" dx dy - Syex! + dy 3X² So ye. 314² dy 4 = site dy A R x = | 2x y=2x [[ ye²d4 = ['ƒ”ª" ye^¹ dydx = ['-—- y^²e²" d dx R |y=0 y 4 y=2x 28²e²dx=3e²-3(e-1). = S₁ 2x² e ³ dx = 2²/ #gesidgate enyi lo-te 3 == X YOY'S nll > x = 1 1:2

請問這題求dy/dx的時候，為什麼不能用隱含數微分法來微？

例1 Find the area of the surface generated by revolving the curve 6xy=x+3 from | |x=1 to x=3 about the x-axis. 【100 成大】 x++3x² 解:6.xy = x + 3 > y= dv 1 1+(2)2 =₁/1+ 1+-x dx 4 所求表面積為 = 1 + 6x 6 2x 1 + 24x² 1 1 2 dy 1 -- dx 2 1 +--- 2x² x+ = 1 2x² 1 ·x² +· 2 2x²

微積分 我想問第（3）題

1. 下列各題:求f(x)在 I 上的所有奇異點,並決定f(x)遞增、遞減的範圍。最後, 作f(x) 值的走勢圖,指出產生相對極值以及絕對極值的地方。 (1) f(x)=x²-3x+6, I = [-2, 2] (2) f(x)=x²-6x²+9x-6,I= [0, 5] (3) f(x)=x²e-*,I=R (4) f(x)=-x°+9x²-15x+10,I= [0, 6]

請問這題要怎麼算～

1 89. Let f be a function such that f'(x): If 1 + x² 0₁5 2 LIFE AND Qurbliet 1 + x² dig(x) = f(2x + 1), what is g'(x)?sup inslissxs) =

想問第4題畫線處 分母(tan²x)-1 =(sin²x/cos²x)-1 =(sin²x-cos²x)/cos²x 為什麼把1/cos²x移到分子以後 分母不是sin²x-cos²x ? 感謝！

x² Example 4 Find lim x 0 sec X 1 SOLUTION The evaluation of this limit requires a little imagination. Since both the numerator and denominator tend to zero as x tends to zero, it is not clear what happens to the fraction. However, we can rewrite the fraction in a more amenable form by multiplying both numerator and denominator by sec x + 1. x2 x² sec x 1 lim x-0 secx 1 - = = x2 sec x 1 - x² (secx + 1) sec² x 1 lim (sin x-0 sin x sec x + 1 sec x + 1) - = Since each of these factors has a limit as x tends to 0, the fraction we began with has a limit: = x² (secx + 1) tan² x - 1 x² cos²x(secx + 1) sin² X 2 (*) ² (cos²x)(secx + 1). 2 ·lim cos²x lim (secx + 1) = (1)(1)(2) = 2. x→0 x ●

第17合成函數前面有函數怎麼做？

8:20 ul 4G o moodle.chu.edu.tw 2.4節(p.154):7、31 1-22 Differentiate. 7. y = sec 0 tan 31. (a) Find an equation of the tangent line to the cury y = 2x sin x at the point (11/2, ). (b) Illustrate part (a) by graphing the curve and the line on the same screen. 2.5節(p.162):17、31 7-48 Find the derivative of the function. 17. h(v) = vž1 + y2 31. y = 1 + sinx COS 2.6節(p.170):31 (本題除了算出切線方程式 要用電腦畫出隱函數曲線與切線) 31. x² + y2 = (2x² + 2y? – x)?, (0,5) (cardioid) YA D 2.9節(p.197) :31、35 31-36 Use a linear approximation (or differentials) to est the given number. 31. (1.999) 35. tan 2° +

第6題求解，謝謝

6. (12%) (a) Find the equation of the line which is parallel to the tangent line to the graph of 2 x y ==+ at the point (2,2) and passes through the point (1,-1). 2 (b) Find the equation of the line which is perpendicular to the line obtained from part (a) and passes through the point (-2,1). y+1=0(2

第二、三題求解，希望有過程拜託🙏

- Reader Touch. 天,然後休假兩天。該飯店客房部需決定至少僱用多少位員工,才能滿足每天的, 需求,試建構此問題之線性規劃模式?(20%) 三 四 五 日 星期 人力需求 14 10 11 13 16 20 18 2. 請分別以(1)高斯-焦丹法(2)克拉瑪法則(Cramer's rule)求解下列方程組。(30%) x1 + x2 + 2x3 = 8 -X1 - 2x2 + 3x3 = 1 3x1 - 7x2 + 4x3 = 10 3.利用M=[A]求出Al。(20%) 11 A= -2 11 11 1」 「1 + 2] ro 這裡輸入文字來搜尋 員 27°C A 6) 英