想問第七題，謝謝🙏

1. 兩函数相交於:(x=-4)=-x+2 0 = -x+2 x=2 S (x+2)-(x²-4)dx 13(x=x+6)dx SONTEX X=021 x x+2x-1 ~= x(x+2)+ S21(-x-x+2x) |dx| x²+x-6= 0 x÷4=0 (x+3)(x-2)=0 a X=11-2 二 (x+2) (x-2)=0 0274 商用微積分 = [x-x+6x] |23 習題 7-5 2125 = 20.8333 = 4 3 求1~5題各曲線所圍成區域的面積。 x²+2x+3= x²-|1. y=x²-4, y=-x+2=2 rX²=rX4; o 3. y=−x²+2x+3, y=x²−1 = 9 4 5.y=e`-1、y=- --1與 x-軸 2(X-2)(x+1)=0 6.求y=ex. i-x=201 et 12 b ·15 37/3 = 3.0833 2.y=x²,y=x²+2x²-2x 4.y=x²,y=2x-x² 215 4. 兩函數交於: x² = 2x= x² 1、xy=1、x=1與x=2等圖形所圍成平面區域的面積。2X-2X=0x=01 2f(xrex+3) 求y=2*.x+y=1、x=1等圖形所圍成平面區域的面積。 -(x²-1) d x =(2x+2x+4)dx y=1-x 19号+2460966 函數的平均值 号:9# 2x(x-1)=0 定義 老

剛開始學隱函數，想問框起來的部分是用什麼rule呢？課程裡面是說用chain rule，但我看不太懂是怎麼寫成那樣的

Example 1: Let x² + y² = 25, , find dy == dx , dx dy and the equation of the tangent at (3, 4). Solution: 2x+2y 33 dy dx = 0 dx 2x dy |+ 2y = 0 X dy m = dx dy dx\(3,4) 3 -¾³½⇒(y−4) = −²/√(x − 3). =- 4 dx dy X

要用什麼test來判斷這題會不會收斂

Z n=2 (Inn)lan

請問這題要怎麼解？（積分）

Evaluate the integrals in to integration by parts. 25. e√3s+9 dsimuzzA monood lon π/3

請問第25怎麼做？

Using Substitution Evaluate the integrals in Exercises 25-30 b to integration by parts. 25. 29v parts.w bonidmo od .1 eV3s+9 dsimuzzA29 26. eA. 9126. 90 S x 0 motorT [stnamebnu π/3 13 C

右下角是解答，但我一直算不出來，請幫我解答一下，還有過程

Apply elementary row operations to transform the following matrix first into echelon form and then into reduced echelon form. 64-5 3 -6 3 -7 -7 8-589 3-9 12-96 15 1 0-2 3 0 -24 0 1 -2 2 0 -7 000014 62 62

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-