求這題詳解（鉛筆部分也是題目）

3. Express the function in the form fogoh. R(x)=x-1 [§1

請問這一題如何計算？

10. ³ [x¹dx=? where [ ] is the greatest integer function. 0 x

想請問（c)要怎麼寫？

EXI. Find the limit : lim(x+3) X-2 lim (x+3) = 5 X-2 Ex2. Find the limitlim ƒ(x) (a) f(x) →2 (a) lim f(x). = 8-72 = x4 X-2 (x+²)(x-2) x=2 = 4 x-4 x-2 X- (b) ƒ(x) = |x-¹| (c) ƒ(x) = (x,x #2 x-2 0,x=2 (b) lim f(x) = X-2 lim f(x) = X-72² D.N.E (x-2) X-2 (x-2) X-2 1 Definition of the Limit of a Function If f(x) becomes arbitrarily close to a single number L as x approaches c from either sid 1"}

81怎麼證明

f at (c, f(c)) is parallel to the tanger 81. Proof Prove that if f is differentiable on (-00,00) and f'(x) < 1 for all real numbers , then f has at most one fixed point. [A fixed point of a function f is a real number c such a that f(c) = c.] = DA TT of Cvornica 81 to show that

求解...

the race. point (0, 2), find f(4) and f'(4). I 37 19. Sketch the graph of a function f for which f(0) = 0, f'(0) = 3, f'(1) = 0, and f'(2) = -1. . nners the - = = -

第六題，怎麼算

6. Suppose that the targent line to the graph of a function f at x = 1 passes through the point (4,9) = and that f(1) = 3. Then f'(1) = 2 JJ斗笠 、恐日頭(60 分)

求解28題 感恩🙇

36. Sup ang 22-25 Explain, using Theorems 4, 5. 7. and 9. why the function is continuous at every number in its domain. State the domain. 2.x2 - x - 1 2 22. F(x) 23. 20) = r2 + 1 By Le (a) (b 24. h(x) = cos(1 – x?) 25. M = N DI 38. W tir 26-29 Use continuity to evaluate the limit. 26. lim x 20 – x2 27. lim sin(x + sin x) ULTET (28) lim x'tan r 11/4 29. lim x®/Vx2 + x - 2 IX 30. Show that f is continuous on (-00, ). 39. S f(x) = x2 if x < 1 x-1 if x>1 31-32 Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the whı sont o LINE TERANG 1633 是

求解第33題 感謝🙇

30. lim x csex 21 29. lim sec ---(4/2)+ x x 22 31. lim x==2 4x + 4 32. lim X-2+ x x² - 2x - 8 x² - 5x + 6 8 33. Find the vertical asymptotes of the function x? + 1 3x - 2.x2 1 ||||| 1 34. Determine lim and lim X-TX r- (a) by evaluating f(x) = 1/(x - 1) for values of x that ap- proach 1 from the left and from the right, (b) by reasoning as in Example 8. 35. (a) Evaluate the function f(x) = x2 - (24/1000) for x = 1.

求解orz

Supose we know that f(x)=x' +2x+1 has an inverse function f !, Then (f !)'(4)=_7 【中正數學】

求解( ･ั﹏･ั)

wy 若 lim f(x)=b,則 微 Let f be twice differentiable function and let u(x)=f(x²-1) if f'(0)=1 , f"(0) = 2 · then u"(1)=_| 【清華經濟】