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

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-

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?

請問綠色框起來的是什麼意思

example.o A,B: sets, |A|-|B|=n<∞ A function f : A → B is one to one Proof (F) Suppose 39, #az & fears = fiaz) : 充分必要 if and only if it is onto. 7-1-4 3 | { bib = fca, for a EA & 979, 192}|≤n-2 =|f(A)| = h-1 < |B| 7 f is not onto Proof