想請問這題這樣做是對的嗎？謝謝🙇

(x+1)² = (x²+2x+1 13. lim x-0 1 x->0 (x+1)² = 1 #1 1 x (x+1)² x+1 = x x(x+1)² lim x-(x+x) = lim x-70 x (x+1)²

不知道怎麼畫 教教我吧 謝謝🙏

8. Sketch the graph of a function y = f(x) that satisfies the following con- ver: ditions: f(0) = 0, lim f(x) = 0, lim f(x) = lim f(x) = ∞ xx x-1- x-1+ lim f(x) = lim f(x) = =-〇〇 x-1+ x-1-

我直接微分可以算出正確答案b，但如果把等號左右一起除x後再微分就算不出來了🥲。 是不能這樣除嗎…（我覺得是可以的吧）還是我哪裡算錯了… btw第一張照片是題目跟解答 第二張是我用同除x的算法！

CHNOLOGY 正確答案: Find dx for xe' + 1 = xy. (a) 0 y - e³ (b) xey -x (c) — x (d) xey 1 (e) None of these O OOO a. b. C. d. e. 你答對了!

請問怎麼由中間那個數字（3210.0123）4 變為左右兩邊的（？）8 、（？）2？真的可以算的出來嗎？

(344.0657 )8-> (3210.0123) 4 (11100100.> 2 84228 828...4 3...4 0-10546872 8 084574976 X 3x442x4+1x4+0x4 =192+32+4=228 e 26228 2/114 0x4+1x4+2x4+3×4-4 3 7 16+ +256 8 674999808 2(57 2128.... 27 " 2560-10546872

感覺這題要用反函數

Finding Values In Exercises 28-30, find f-1(a) for the function f and real number a. Function 30. f(x) = x³ - Real Number 4 x > 0 a = 6 X

怎麼解？

2. For what value of a and t does the equation |t-a-a-t hold?

請問綠色框起來的是什麼意思

example.o A,B: sets, |A|-|B|=n<∞ A function f : A → B is one to one Proof (F) Suppose 39, #az & fears = fiaz) : 充分必要 if and only if it is onto. 7-1-4 3 | { bib = fca, for a EA & 979, 192}|≤n-2 =|f(A)| = h-1 < |B| 7 f is not onto Proof

請問圈起部分是看整體（x+1)/(x-1)=1還是分成1/(x+1)+(-1)/(x+1)=0，謝謝

f(x)=1+X+x(x+1)+x(x+1xx+2) 特徵 f(-1)=0 F(-1) = 1 f(x)-f(-1) X+1 十 2! = l 1+x+ x+1 ti f(4) =? 31 求 X(X+1)X(X41XX+2), X+1 袋 EDO 31 -0 21 X+ 1 + 3! (X+1) 2! 3! (叉+15 F X ✗ X+L 2! +8 31

求13,14🙏

$12. 14. x² ex/4 1 dx x(ln x)³ dx 3 43. fl In(t + 1) dt Sxin 15. x(ln x)² dx

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