微積分求解

8. [0/8 Points] Consider the following limit. DETAILS lim Ax-0+ lim Ax-0+ Submit Answer 8 X + Ax Ax Simplify the rational expression as much as possible. 8 x(x + Ax) X 8 X PREVIOUS ANSWERS X Evaluate the one-sided limit. (If an answer does not exist, enter DNE.) DNE LARCALC12M 1.4.029.EP.

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 ●

求解第24題

t (a), explain wh 2+x-6 x-2 lim (x + 3) imit, if it exists. 12. lim x² - 4x x-1 x²-3x - 4 14. lim 2x² + 3x + 1 2 x-1 X² 2x - 3 16. lim 18. lim h→0 20. lim X→-1 22. lim u-2 24. lim t-0 (2 + h) - 8 h 3x - 4 28. lim h→0 x² + 2x + 1 .4. - 1 26. lim x--4 (1 t 4u + 1 u - 2 3 t² + t x²+9-5 x + 4 1 (x + h)² h 1 X Illustrate tion of th 33. If 4x 34. If 2x - 35. Prove 36. Prove 37-42= explain 37. lim 39. 41. 43

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 請問這題怎麼寫～

13. If statement q has the truth value 1, determine all truth value assignments for the primitive statements, p, r, and s for which the truth value of the statement (q + V r) 4-s] A[ → (719)] 13 O o - und is 1. vry n shit zung ->

請問這題怎麼解🙏🙏

15) J Hit dx VX+1 + 5X

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24題的解題思路是什麼？看了很久還是不知道從哪裡開始🤔

Finding an Indefinite Integral in Exercises 17–26, find the indefinite integral. 4x² dx 18. dx W] 116 M 19. √1- x² •dx x4 S Juta 20. Invatta Jose 22. Jest - er de dx (4x² + 9 21. -3 (x² + 3) 3/2 dx e2x dx 23. 1 4 + 4x² + x4 dx 2 x² + x + 1 dx xt + 2x² + 1 1 ***