微積分求救！

MGT Calculus Homework Assignment 3 5. Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, given an example to show why it is false. If f(x) = πª, then f'(x) = xπª-¹. False 7 [$3.1 - 77] 6. F

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. =

求解找極限函數值或者為什麼不存在，還有想問x->-3右上的正號與x->-3有甚麼區別？還有b連題目都不太了解要求什麼,c的話有哪些不是連續的？求求各位大神了🙏

20. The graph of f is given. (a) Find each limit, or explain why it does not exist. (i)_lim_ƒ(x) x−2+ (ii) lim_ f(x) x--3+ (iii) lim f(x) x--3 (iv) lim f(x) X→4 (v) lim f(x) x->0 0 (vi) lim f(x) x→2- (b) State the equations of the vertical asymptotes. (c) At what numbers is f discontinuous? Explain.

請問c7.的domain和range 是這樣寫嗎？

f(x1= Di R x 2 -2 YER X20 TECH TUTOR is the range range of f1 is the domain of f, which 2.00). ✓ Checkpoint 7 Worked-out solution available at LarsonAppliedCalculus.com Find the inverse function of f(x) = x² + 2 for x ≥ 0. After you have found an inverse function, you should check your results. You can ƒ-¹ are reflections check your results graphically by observing that the graphs of ƒ and

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

朋友，想問一下你的數學導論筆記本是用那一本書的呢？至少可以了解多一點點，來自清華大學的同學，謝

Proposition (Statement.). Def. A proposition is a sentence that has exactly one K true value. It is either true, denoted by T, or false, denoted by F 2 ex "7² = 49" true value = T. "2|7" True value = F. "x²= 36" not a proposition. (proposition form). "She lives in Hsinchin not a proposition. 11

沒給角度要怎麼算啊?

Force R is the resultant of two forces P and Q. If the magnitudes of R and Q are 15 N and 7.32 N, respectively, determine (a) the magnitude of P; (9.93 N or 17.25 N) (b) the projection of R onto the direction of P. (13.6 N) B P 0 a R

求解第二題！ （因為圖片要兩題一起看所以順便拍進來了）

§ 1.1 An Intuitive Introduction to Limits For Exercises 1 and 2, use the graph of the function f to determine whether each statement is true or false. Explain.(從圖形決定極限) 1. O lim f(x)=XX/ x→-3+ lim f(x) = 1. x→2 2. a) lim f(x)=1. x-→-3+ e) lim f(x) does not exist. x →4+ c) lim f(x) = 2. x->2 b) lim x->0 flim f(x) = 3. x-5 d) lim f(x) = 3. x-4 f(x) = 2. Xe) lim f(x) does not exist. x →3 lim f(x) = 2. X→4 S b) lim f(x) = f(0). x->>0 d) lim f(x)=3. x->2* y 4 3 234 y = f(x)

求解釋這一題 看不太懂😭

例題:【反函數】 若f(x) = x²,f:[0,3]→[09],求 f(x)的反函數。 2: To9]→{0.3] 解: f(x) = x 在 [0,3]上為1-1 函數,取f'(x) = x,則有 f(f'(x)) = (√x)} = =x, ∀x∈[0,1] 345 S' (f(x))=√x² = =x,∀x∈[0,0],故f(x) 的反函數為」。 f(x)=xx 2:57/9:52 y X

請問這題求dy/dx的時候，為什麼不能用隱含數微分法來微？

例1 Find the area of the surface generated by revolving the curve 6xy=x+3 from | |x=1 to x=3 about the x-axis. 【100 成大】 x++3x² 解:6.xy = x + 3 > y= dv 1 1+(2)2 =₁/1+ 1+-x dx 4 所求表面積為 = 1 + 6x 6 2x 1 + 24x² 1 1 2 dy 1 -- dx 2 1 +--- 2x² x+ = 1 2x² 1 ·x² +· 2 2x²