[考題] 基礎數學/1002期中考/陳政輝
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 │
└ ┘
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※ 編輯: Cindy20231 來自: 220.140.196.34 (06/26 15:17)
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