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 )

這題的解答給的是C, 該怎麼求出，感謝！

6. Find the volume of the solid whose region is the intersection of the cube {(x, y, z) : |x| ≤ 1, |y| ≤ 1, || ≤ 1} and the ball {(x, y, z) = x² + y²+ z² < 2}. 16 (A) 32(√2-1). (B) (8-√2). 3 16 (C) (10- √2)TT. (D) √√2π. 3 32 3

求解25、29跟32

108 13. lim 15. lim 17. lim 19. lim 818 21. lim x18 CHAPTER 2 23. lim 31² + aitab od n61² + 1 - 5 lin 1³ - 4t + 1 14. lim 9-2/² n r - p³ 2² + 3r³ 4-√√√x 2 + √√x √x + 3x² 4x 1 √1 + 4x6 2-x² (12 saior,558) 2x5 - X x→→∞ x² + 3 26. lim (√x² + ax X-8 27. lim (x - √x) x →8 25. lim (√25t² + 2 − 5t) 1900 29. lim (e-2x cos x) X18 31. lim esec x X→(π/2) + - L 33. (a) For f(r) = LIMITS AND DERIVATIVES OT32 X M mbinogest 20 16. lim 18. 3x³8x + 2 x→∞ 4x²³5x² - 2 20. lim 1-8 lim →20 22. lim 8118 yd boonlqs ei 24. lim √x² + bx) 32. lim [ln(1 + x²) − In(1+x)] - x18 (u² + 1)(2u² - (u² + 2)² t + 3 odme 30. lim √21² - 1 √√1 + 4x6 2 - x² ledre att n q³ + 69 - 4 q→∞ 4q² − 3q + 3 SO 28. lim (x² + 2x²) 8118 1- e* *→∞ 1 + 2e*

想問一下這題 因為課本沒有解答也不知道自己算得對不對

16. Chemistry: Wind Chill At 0° Celsius, the heat loss H (in kilocalories per square meter per hour) from a person's body can be modeled by notenui ent to VID N ov x3 ml H = 33(10√v − v + 10.45) where v is the wind speed (in meters per second). dH (a) Find and interpret its meaning in this situation. dv zive (b) Find the instantaneous rates of change of H when v = 2 and v 5. =

求這題～ 答案為為 a .31cm b.866J c.1.15J

ping. What was the initial speed of the bullet? 8.43 A Ballistic Pendulum. A 12.0 g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 9.00 kg, suspended from a cord 70.0 cm long (see Example 8.8 in Section 8.3). Compute (a) the vertical height through which the pendulum rises, (b) the initial kinetic energy of the bullet, and (c) the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the wood. 150 kg block is attached A

想請問這題🙏

57. The series 2x5 17x7 62x⁹ + + 3 15 315 2835 converges to tan x for -π/2 < x < π/2. a. Find the first five terms of the series for In | sec x|. For what values of x should the series converge? tan x = x + + b. Find the first five terms of the series for sec² x. For what values of x should this series converge? c. Check your result in part (b) by squaring the series given for sec x in Exercise 58.

求解第3、4題🙏 證明題總是卡住...

3. Let Bo and ₁ denote the least squares estimators of Bo and 3₁. Define SSE = Σ(Yi-Bo- i=1 B₁X₁)². Show that (a) E (SSE) = 0², (b) cov(Y, ₁X) = 0. 4. In Section 10.4, we defined a test statistic where s² = T = VSEZ SSE. In addition, it is known that T~: n-2' (a) Show that (1) can be re-written as 1 tn-2. T = r√n-2 (1) (2) (b) Use Part (a) to test Ho: p = 0 vs H₁ p 0. [Hint: (2) can be regarded as a test statistic under Ho.]

請問根據(f)小題我求出的s，怎麼進行一階和二階微分？

(e) (6%) Find the inverse demand function p =D (q), and write down both the domain and range for D (q). 1 (f) (10%) Given the inverse demand function obtained above, and note that the sales revenue of the firm is given by s = p(q) x q. Find both the first- and second-derivatives of s with respect to p, i.e., s' (q) and s" (q).

為什麼c第一行 x平方加一後 不用三次方

(b) U=X X X = asu dy dy du √3x + 2x - 1) == dx = du dx (Let U= 3x²+2x-1 & Y = √U = U²) 3 (tan tan' (171)) (0) = (dam (1) =U³² · (6x + 2) = = (3x + 2xX-1) ³ ((x+²) Q dy_ dy dw dy = (3u²) (seciul) (2x) 1 - dx 2 [let X=X+1, w=fonu, y=w² UX [x→u →W+Y] = 3 tan(x²1)- sec ²(x+³1) (2x)

請問為什麼f（x）微分不是 e'x+Xe'x-1 而是 e'x+Xe'x 呢

the line for two lines that are 3x² + 3x - 3 and p e curve y = 1 + 2e e 3x - y = 5? Illus es. 2x+y=1. normal line to the c e to the parabola y e parabola a secon ere are two tanger rough the point (0. where these tang ough the point (2, x² + x. the point (2, 7) tha diagram to see w that if f(x) er R Ex3 (1) If f(x)=xe* find f(x) and f(x) f'(x) = e^ + xe^ = (1+x). e* => f"(x) = e² + [e^ + xe*] {"(x) = # Hence, f^(x) = (n+x) ex