想請問紅色的地方要怎麼變藍色的

EXAMPLE 3 Solution We differentiate the equation implicitly. (AS) ² = x² + sin.xy d VIR SY d (²) - (x²)+(sin xy) = dx dx Find dy/dx if y² = x² + sinxy (Figure 3.31). d dx dy dx 2y = d 2x + (cos xy) (xy) dx ansa to along or see anuar Differentiate both sides with respect to x... ... treating y as a function of x and using the Chain Rule.

請問有人知道怎麼算嗎？拜託了🙏

11. [-/6 Points] DETAILS Find the constants a and b such that the function is continuous on the entire real line. a = b = LARCALC12M 1.4.073. 5, f(x) = ax + b, -5, 13 X ≤-2 -2<x<3 X23

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 ●

第一行是題目 第二行是給的詳解 我從第一步就不懂 為什麼要假設成L?🤨 後面也看不懂QWQ

Question Limit. 4. Find the humber c such that lim 3x²+CX+c+3 X-7-2 X²+X-2 exists and evaluate this limit. lim A = Suppose X+2+x²+x-2² = L. We have that lim (3x+exto+ 3) = lim (2xxxx112 x (x²7x²)) X7-2 x=-2 X+X-2 3x²+x+c+3 = ( Lim Xxx-9²³) x (&im₂ (X+X-2)) = Lx0=0 X-7-2 => 3x(-2)² + cx (-2) + C+3=15-C=O=> C=15

請問第41題這種類型的題目要怎麼解🙏🙏

41-44 Use implicit differentiation to find az/ax and az/ay. .2 41. x² + 2y² + 3z² = 1 (42. x² - y² + z² – 2z = 4 (43) e² = xyz 44.) yz + x ln y = z²

請問第六和第十題如何計算？ 大學微積分 Integration by parts

S. cite the formula for integration by parts. plain how you would choose u and du when using the egration by parts formula. Illustrate your answer with ar Exercises es 1-28, find each indefinite integral. 32. x dx -X 35. F. et dx - tc th - x)² dx 36. F. tc 1) ex dx th - 2. { xe* dx 4. S 6xe* | * dx 6. [(e-* + x) dx 8. S (x – 3)e% de 10. S x(x + 4)-2 dx . 14. S x? In 2x dx 16. Vx In x dx + 1)-32 dx 37. F f f E-5 dx 12. 3x V2x + 3 dx 38. F f f 2x dx 39. V af x dx 1

離散數學第二章 邏輯的基本原則 請問這題的b怎麼算

19. Provide the steps and reasons, as in Exercise 18, to establish the following logical equivalences. a) p V [p ^ (p V q)] p lorer v b) p va v (p^^r) A p Vavr c) [(-pv-q) → (p^q^r)] paq 20. Şimplify each of the networks shown in Fig. 3.

離散數學 第一章 請問第19題怎麼算 第二張是答案可以參考

19. How many times is the print statement executed for the following program segment? (Here, i, j, k, and m are integer variables.) ni diaq orta ) for i:=1 to 20 do as U = for j := 1 to i do for k := 1 to j do for m:= 1 to k do groll print (i* j) + (k * m)

請問第13題的b怎麼算 離散數學第一章 第二張是答案可以參考～

b) X, 2-3, 3i 35 ; 1< 13. In how many ways can we distribute eight identical white balls into four distinct containers so that (a) no container is left empty? (b) the fourth container has an odd number of balls in it? nansion of

請問這兩題怎麼解？🙏

13、 X150 =x-y find x e y $4 X xe y * * , e - | yet y find tangent line at (at o.lt