想問這題要怎麼解 只有想到要用左右極限相等

15. Let x cot kx if x < 0 = (2.0) if x ≥ 0 EURCHSHA Find the value of c that will make f continuous at x = 0. FIGURS Glaidw |[ 2.0] to unioqbim srb (7) f(x) Jx L x ² + c =

這題要怎麼證明

53. Give a rigorous proof that if lim f(x) = A and lim g(x) = B, then 818 818 imorob bas tot lim [f(x) + g(x)] = A + B 818

求這題 a 12 b 8

Farry Find the values of the constants a and b such that lim 2 Hint: Use the formula ³ - ³ = (a - b)(a² + aß + 3²)) Vax+b-2 1.

求這題～～～

9. Let f(x): = 1 , f(0) = 0 7 dx fixty) = ax (tex) +Pay) +zry) = f(x+y) dx dx for x > 0. Show that the area of the triangle, which is X bounded by any tangent line to the curve of f and the two coordinates + axes, is of 2 square units. f(0) = 0 {x

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)

求過程 算到最後卡住了

To 1-3 -1 301 | R₂ + ZR₁ Brok: 02 6 1-5 0 - R3-R1 03-924 |-|| R4 +R₁ N 2₁ R₁ - R₂ R3+5R₂ T 0-1 3 1 3 2 01-302 ött 00 32 | 1 。 O 0622 -R2- 0 CONCE 1-3 -1 30 17 000 5-51-4 0000622 200 1-10-1 22 11

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

（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