請問這題怎麼算

9. A rectangle is inscribed in a right triangle, as 000,00 shown in the accompanying figure. If the triangle 0 has sides of length 5, 12, and 13, what are the

請問這題怎麼算

1. What number exceeds its square by the largest amount? [Hint: Find the number x that maximizes trigin f(x) = x = x².] bas auoivdo líssi jon - sidan Enter Chaigh ot by

想請教這一題微積分，謝謝！

2. (8%) Consider a real numbers and suppose that lim x→0√√x+s4-s² find s (there are two possible answers). = 3,

請教這題a,b小題 不知道怎麼列式子

4.21. Suppose that P{X=a}=p, P{X=b} = 1 - p (a) Show that X-b is a Bernoulli random variable. (b) Find Var(X).

請問這題的過程怎麼計算～ 題目是要求二次導函數及最大最小值 （照片黑色部分是題目 藍色部分是解答）

No. Date (37₁flx) = (x-2)³ x² fix)= 241X22) 74 (a-b) ² = a ²³-3a²b+3ab²-6³ svitalar maximum at (-4, -13,5) quitalay Test fails for x=2₁

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

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 ●

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