想問這題怎麼算

28. A trough is 6 m long and its ends have the shape of isos- celes triangles that are 1 m across at the top and have a height of 50 cm. If the trough is being filled with water at a rate of 1.2 m³/min, how fast is the water level rising when the water is 30 centimeters deep? goal: dh dt

想問這題要怎麼算🙇‍♀️

37. Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the ranges which follow. LO 5 a. 20 to 40 b. 15 to 45 c. 22 to 38 d. 18 to 42 e. 12 to 48

想請問這兩題要怎麼求出導函數？ 謝謝🙏🏻

12X+1 x 在習題 25-26中求dy/dx。 25. y=(x+1)²(2x-3)³ (x²+1) 8 26. y= (x²+3)³ (x+1)² 2x+7

救救我要怎麼求證 大大感謝

1. it is · (f(x)g(n))²= f'(x)g(n) + fox gix fix) 2. uit 1 3 VEDA (for) ]' f'(x) g(x)-fix) g(x) g(x) g(x)

請問這個怎麼證明🙏🏻 謝謝

1.試證: lin 000 sino D = 2. { [sin(x)] = cos(x) : Hirt & Aist

想請問這兩題微積分怎麼解🙏🙏

113年度作業一 隱函數 1. Find the tangent line of the curve (Implicit Differentiation) sin(xy2) + x²+x+1 = 2y2 at y" (2,-1.99883) 2. Given f(x) = = d (Hint: In(u) = dx x² (1-x)³ sec-1(1+x) 1 du u dx , d dx , find f" (2). sec-1 (u) 1 du = |u|√u²-1 dx , |u|> 1 )

不知道怎麼畫 教教我吧 謝謝🙏

8. Sketch the graph of a function y = f(x) that satisfies the following con- ver: ditions: f(0) = 0, lim f(x) = 0, lim f(x) = lim f(x) = ∞ xx x-1- x-1+ lim f(x) = lim f(x) = =-〇〇 x-1+ x-1-

我直接微分可以算出正確答案b，但如果把等號左右一起除x後再微分就算不出來了🥲。 是不能這樣除嗎…（我覺得是可以的吧）還是我哪裡算錯了… btw第一張照片是題目跟解答 第二張是我用同除x的算法！

CHNOLOGY 正確答案: Find dx for xe' + 1 = xy. (a) 0 y - e³ (b) xey -x (c) — x (d) xey 1 (e) None of these O OOO a. b. C. d. e. 你答對了!

感覺這題要用反函數

Finding Values In Exercises 28-30, find f-1(a) for the function f and real number a. Function 30. f(x) = x³ - Real Number 4 x > 0 a = 6 X

怎麼解？

2. For what value of a and t does the equation |t-a-a-t hold?