[考題] 基礎數學/1002期中考/陳政輝

[Cindy20231 (喵喵)]

You will NOT earn any credits unless you show the intermediate steps to
obtain your solution and the final solution is exactly correct.


(1) (16 points) Apply the Gauss-Jordan method to find the inverse of the
following matrix

A= ┌     ┐
   │1 1 1│
   │0 2 3│
   │5 5 1│
   └     ┘

(2) (7 points for each sub-problem) find dy/dx.

(a) y =  lnx
       ∫     e^(-t) dt, x>0
         2

(b) y =  3x+2
       ∫     (1+t^3) dt.
         0

(3) (7 points for each sub-problem) Evaluate the integral.

(a) ∫xcos(x^2-1)dx　　　　  　(b) ∫(x-1) / (1+4x-2x^2) dx

(c) ∫[sex(x‧e^tanx)]^2 dx    (d) ∫(√1+lnx)‧lnx/x dx

(e)   π/6                     (f)  3
    ∫      (sinx)^2‧cosx dx     ∫  x^2‧e^(-x) dt
      -π/6                         0

(g)    π                      (h)  π/4
    ∫   (e^cost)‧sin(2t) dt     ∫     2x‧cosx dx
       0                            0

(i) ∫sin(lnx)dx               (j)  2
                                  ∫  ln(x^2‧e^x)dx
                                    1

(4) (10 points) Find the eigenvalues and their corresponding eigenvectors of
the matrix

A= ┌     ┐
   │ 1 1 │
   │-2 4 │
   └     ┘

--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.140.196.34
※ 編輯: Cindy20231      來自: 220.140.196.34       (06/26 15:17)
推 KnightZX:推學妹認真!基數有新的進展了@@
推 PTTjoker:推~