求b小題

dt' Find the equations of the tangent and normal line at the indicated point. (a) x² + y² = 169, (5, 12) (b) z² + z tan ¹y=y> 1, (−1)

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

想請問第59.61題要怎麼算？求解🙏🥹

59. lim Ax-0 61. lim Ax-0 62. lim Ax-0 2(x + Ax) - 2x Ax DAIWS 60. lim (x + Ax)³ = x³ Ax Ax-0 (x + Ax)² - x² Ax odi (x + Ax)² = 2(x + Ax) + 1 - (x² - 2x + 1) Ax niz x angemi ya

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. =

（大一微積分） 請問這題這樣寫正確嗎？背流程寫的😅，圖一為需用到的定義 正確的話，想問紅色圈圈的1是怎麼來的？

DEFINITION Let f be a function defined on some open interval that con- tains the number a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a is L, and we write lim f(x) = L x→a if for every number &> 0 there is a corresponding number 8 >0 such that | ƒ(x) − L| < ɛ if 0 < x-a <8 then

三角函數微積分請益 謝謝🙏

sin 8x cos 5x dx

求解答，二變數函數的偏微分

du 2. u=x² * (1) x (2) du dy du (3) dz

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

想問第三行到第四行 為什麼後面的三次方不見了

Y 例題:【微分連鎖律】 請微分f(x) = (x²+3x)*(5x+2)。 解: f'(x)=((x²+3x)*)'(5x+2)+(x²+3x)*(5x+2)' = 3(x² + 3.x)² (x²+3x)'-(5x+2)+(x²+3x)*(5) = 3(x² + 3x)² (2x+3) (5x+2)+(x²+3x)*(5) = (x² + 3x)² ((6x +9). (5x+2)+(5x² +15x)) = (x² +3x)*(35x² +72x+18) 例題:【微分連鎖律】 請微分f(x)=xx+1.(x²+1)*。