MATLAB揭秘--第五章习题

• 1

octave:7> s = 7*sqrt(2)-5*sqrt(60)+5*sqrt(8)
s = -14.688

• 2

octave:9> syms x;
octave:10> q = 3*x.^2+2*x;
octave:11> s = solve(q==7)
s = (sym 2×1 matrix)

  ⎡  1   √22⎤
  ⎢- ─ + ───⎥
  ⎢  3    3 ⎥
  ⎢         ⎥
  ⎢  √22   1⎥
  ⎢- ─── - ─⎥
  ⎣   3    3⎦

• 3

octave:15> syms x;
octave:16> q = x.^2+sqrt(5)*x-pi;
octave:17> s = solve(q)
s = (sym 2×1 matrix)

  ⎡         _________⎤
  ⎢  √5   ╲╱ 5 + 4⋅π ⎥
  ⎢- ── + ───────────⎥
  ⎢  2         2     ⎥
  ⎢                  ⎥
  ⎢    _________     ⎥
  ⎢  ╲╱ 5 + 4⋅π    √5⎥
  ⎢- ─────────── - ──⎥
  ⎣       2        2 ⎦

• 4

octave:19> syms x;
octave:20> q = sqrt(2*x-4);
octave:21> s = solve(q==1)
s = (sym) 5/2

• 5

octave:23> clear
octave:24> syms t;
octave:25> q = 2*t.^3-t.^2+4*t-6;
octave:26> s = solve(q)
s = (sym 3×1 matrix)

  ⎡                     _____________                                    ⎤
  ⎢1   ⎛  1   √3⋅ⅈ⎞    ╱ 289   √2658                    23               ⎥
  ⎢─ + ⎜- ─ - ────⎟⋅3 ╱  ─── + ─────  - ─────────────────────────────────⎥
  ⎢6   ⎝  2    2  ⎠ ╲╱   216     36                         _____________⎥
  ⎢                                        ⎛  1   √3⋅ⅈ⎞    ╱ 289   √2658 ⎥
  ⎢                                     36⋅⎜- ─ - ────⎟⋅3 ╱  ─── + ───── ⎥
  ⎢                                        ⎝  2    2  ⎠ ╲╱   216     36  ⎥
  ⎢                                                                      ⎥
  ⎢                                                         _____________⎥
  ⎢1                   23                  ⎛  1   √3⋅ⅈ⎞    ╱ 289   √2658 ⎥
  ⎢─ - ───────────────────────────────── + ⎜- ─ + ────⎟⋅3 ╱  ─── + ───── ⎥
  ⎢6                       _____________   ⎝  2    2  ⎠ ╲╱   216     36  ⎥
  ⎢       ⎛  1   √3⋅ⅈ⎞    ╱ 289   √2658                                  ⎥
  ⎢    36⋅⎜- ─ + ────⎟⋅3 ╱  ─── + ─────                                  ⎥
  ⎢       ⎝  2    2  ⎠ ╲╱   216     36                                   ⎥
  ⎢                                                                      ⎥
  ⎢                                             _____________            ⎥
  ⎢                       23            1      ╱ 289   √2658             ⎥
  ⎢            - ──────────────────── + ─ + 3 ╱  ─── + ─────             ⎥
  ⎢                     _____________   6   ╲╱   216     36              ⎥
  ⎢                    ╱ 289   √2658                                     ⎥
  ⎢              36⋅3 ╱  ─── + ─────                                     ⎥
  ⎣                 ╲╱   216     36                                      ⎦

• 6

octave:29> clear
octave:30> syms x y z;
octave:31> a = x-3*y-2*z;
octave:32> b = 2*x-4*y-3*z;
octave:33> c = -3*x+6*y+8*z;
octave:34> s = solve(a==6,b==8,c==-5)
s =
  scalar structure containing the fields:
    x =
      <class sym>
    y =
      <class sym>
    z =
      <class sym>
octave:35> x = s.x,y = s.y,z = s.z
x = (sym) 1
y = (sym) -3
z = (sym) 2

• 7

>> syms x;
>> q = exp(x)-x.^2;
>> s = solve(q==0) 
s = 
 -2*lambertw(0, -1/2)
  -2*lambertw(0, 1/2) 
>> double(s)
ans =
   1.5880 - 1.5402i
  -0.7035 + 0.0000i

• 8

>> syms x;
>> q = tan(x).^2-sec(x).^2;
>> s = simplify(q) 
s = 
-1

• 9

>> syms x;
>> q = taylor(tan(x),10)

q = 
x + x^3/3 + (2*x^5)/15 + (17*x^7)/315 + (62*x^9)/283

• 10
  刚刚电脑突然卡死，MATLAB的数据也丢失了，就用网上的在线编辑器弄出了答案：

octave:37> clear
octave:38> syms x;
octave:39> q = 4/(5-cos(x));
octave:40> s = taylor(q,'order',10,'expansionpoint',0)
s = (sym)

       8        6      4    2    
  241⋅x    113⋅x    5⋅x    x     
  ────── - ────── + ──── - ── + 1
  258048   23040    192    8