미분적분학실습2-Week-1

915 days ago by jhlee2chn

구의 그래프  $x^2 + y^2 + z^2=1$

implicit_plot3d(x^2+y^2+z^2==4, (x, -3, 3), (y, -3,3), (z, -3,3)) 
       
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var('x,y,z') implicit_plot3d(x^2==3*y^2+2*z^2, (x, -3, 3), (y, -3, 3), (z, -3, 3), opacity=0.5) 
       
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sqrt(2) in RR 
       
True
True
i^3 
       
-I
-I
3 + 2*i in CC 
       
True
True
[1, 1.1..10] 
       
[1.00000000000000,
 1.10000000000000,
 1.20000000000000,
 1.30000000000000,
 1.40000000000000,
 1.50000000000000,
 1.60000000000000,
 1.70000000000000,
 1.80000000000000,
 1.90000000000000,
 2.00000000000000,
 2.10000000000000,
 2.20000000000000,
 2.30000000000000,
 2.40000000000000,
 2.50000000000000,
 2.60000000000000,
 2.70000000000000,
 2.80000000000000,
 2.90000000000000,
 3.00000000000000,
 3.10000000000000,
 3.20000000000000,
 3.30000000000000,
 3.40000000000000,
 3.50000000000000,
 3.60000000000000,
 3.70000000000000,
 3.80000000000000,
 3.90000000000000,
 4.00000000000000,
 4.10000000000000,
 4.20000000000000,
 4.30000000000000,
 4.40000000000000,
 4.50000000000000,
 4.60000000000000,
 4.70000000000000,
 4.80000000000000,
 4.90000000000000,
 5.00000000000000,
 5.10000000000000,
 5.20000000000000,
 5.30000000000000,
 5.40000000000000,
 5.50000000000000,
 5.60000000000000,
 5.70000000000000,
 5.80000000000000,
 5.90000000000000,
 6.00000000000000,
 6.10000000000000,
 6.20000000000000,
 6.30000000000000,
 6.40000000000000,
 6.49999999999999,
 6.59999999999999,
 6.69999999999999,
 6.79999999999999,
 6.89999999999999,
 6.99999999999999,
 7.09999999999999,
 7.19999999999999,
 7.29999999999999,
 7.39999999999999,
 7.49999999999999,
 7.59999999999999,
 7.69999999999999,
 7.79999999999999,
 7.89999999999999,
 7.99999999999999,
 8.09999999999999,
 8.19999999999999,
 8.29999999999999,
 8.39999999999999,
 8.49999999999999,
 8.59999999999999,
 8.69999999999999,
 8.79999999999999,
 8.89999999999999,
 8.99999999999999,
 9.09999999999999,
 9.19999999999999,
 9.29999999999998,
 9.39999999999998,
 9.49999999999998,
 9.59999999999998,
 9.69999999999998,
 9.79999999999998,
 9.89999999999998,
 10.0000000000000]
[1.00000000000000,
 1.10000000000000,
 1.20000000000000,
 1.30000000000000,
 1.40000000000000,
 1.50000000000000,
 1.60000000000000,
 1.70000000000000,
 1.80000000000000,
 1.90000000000000,
 2.00000000000000,
 2.10000000000000,
 2.20000000000000,
 2.30000000000000,
 2.40000000000000,
 2.50000000000000,
 2.60000000000000,
 2.70000000000000,
 2.80000000000000,
 2.90000000000000,
 3.00000000000000,
 3.10000000000000,
 3.20000000000000,
 3.30000000000000,
 3.40000000000000,
 3.50000000000000,
 3.60000000000000,
 3.70000000000000,
 3.80000000000000,
 3.90000000000000,
 4.00000000000000,
 4.10000000000000,
 4.20000000000000,
 4.30000000000000,
 4.40000000000000,
 4.50000000000000,
 4.60000000000000,
 4.70000000000000,
 4.80000000000000,
 4.90000000000000,
 5.00000000000000,
 5.10000000000000,
 5.20000000000000,
 5.30000000000000,
 5.40000000000000,
 5.50000000000000,
 5.60000000000000,
 5.70000000000000,
 5.80000000000000,
 5.90000000000000,
 6.00000000000000,
 6.10000000000000,
 6.20000000000000,
 6.30000000000000,
 6.40000000000000,
 6.49999999999999,
 6.59999999999999,
 6.69999999999999,
 6.79999999999999,
 6.89999999999999,
 6.99999999999999,
 7.09999999999999,
 7.19999999999999,
 7.29999999999999,
 7.39999999999999,
 7.49999999999999,
 7.59999999999999,
 7.69999999999999,
 7.79999999999999,
 7.89999999999999,
 7.99999999999999,
 8.09999999999999,
 8.19999999999999,
 8.29999999999999,
 8.39999999999999,
 8.49999999999999,
 8.59999999999999,
 8.69999999999999,
 8.79999999999999,
 8.89999999999999,
 8.99999999999999,
 9.09999999999999,
 9.19999999999999,
 9.29999999999998,
 9.39999999999998,
 9.49999999999998,
 9.59999999999998,
 9.69999999999998,
 9.79999999999998,
 9.89999999999998,
 10.0000000000000]
[sin(i) for i in range(0, 10)] 
       
[0, sin(1), sin(2), sin(3), sin(4), sin(5), sin(6), sin(7), sin(8),
sin(9)]
[0, sin(1), sin(2), sin(3), sin(4), sin(5), sin(6), sin(7), sin(8), sin(9)]
A = Set([2,3,3,3,2,1,8,6,3]) print A print A.cardinality() 
       
{8, 1, 2, 3, 6}
5
{8, 1, 2, 3, 6}
5
10 in A 
       
False
False
B = Set([8,6,17,-4,20, -2 ]) B 
       
{17, 20, 6, 8, -4, -2}
{17, 20, 6, 8, -4, -2}
A.union(B) 
       
{1, 2, 3, 6, 8, 17, 20, -4, -2}
{1, 2, 3, 6, 8, 17, 20, -4, -2}
s = 34 s 
       
34
34
t = 7 t = t + 1 t 
       
8
8
f(x) = x^2 + x + 1 f(3) 
       
13
13
plot(2*x^3+3*x^2-5*x-6, (x, -3, 3), ymax=20, ymin=-20) 
       
f(x) = 2^x g(x) = 2^x + 2 h(x) = 2^(x+1) - 2 plot(f(x), (x, -3, 3)) + plot(g(x), (x, -3, 3), color='red') + plot(h(x), (x, -3, 3), color='black') 
       
f(x) = (x^3 + x^2 + x)/(x^2 - x -2) plot(f(x), (x, -5, 5), ymin=-20, ymax=20, detect_poles='show') 
       
f(x)=log(x, 2) g(x)=log(x-2, 2) h(x)=log(x, 2)+3 t(x)=log(x-2, 2)+3 p1=plot(f(x), (x, 0, 5)) p2=plot(g(x), (x, 2, 5), color='red') p3=plot(h(x), (x, 0, 5),color='black') p4=plot(t(x), (x, 2, 5), color='green') p1+p2+p3+p4 
       
p1=plot(sin(pi*x-pi), (x, -1, 1), color='red', thickness=3) p2=plot(cos(pi*x-pi), (x, -1, 1), thickness=3) p1+p2 
       
solve(x^2 - 3*x - 2 == 0, x) 
       
[x == -1/2*sqrt(17) + 3/2, x == 1/2*sqrt(17) + 3/2]
[x == -1/2*sqrt(17) + 3/2, x == 1/2*sqrt(17) + 3/2]
solve(x^2 - 3*x + 2 <= 0, x) 
       
[[x >= 1, x <= 2]]
[[x >= 1, x <= 2]]
var('x, y') solve(3*x - y == 2, y) 
       
[y == 3*x - 2]
[y == 3*x - 2]
solve([2*x + y == -1, -4*x - 2*y == 2], x, y) 
       
[[x == -1/2*r1 - 1/2, y == r1]]
[[x == -1/2*r1 - 1/2, y == r1]]
solve([2*x - y == -1, 2*x - y == 2], x, y) 
       
[]
[]
var('x, y, z') solve([2*x + 3*y + 5*z == 1, 4*x + 6*y + 10*z == 2, 6*x + 9*y + 15*z == 0], x, y, z) 
       
[]
[]
var('t') solve(abs(t-7)>=3, t) 
       
#0: solve_rat_ineq(ineq=abs(_SAGE_VAR_t-7) >= 3)
[[t == 10], [t == 4], [t < 4], [10 < t]]
#0: solve_rat_ineq(ineq=abs(_SAGE_VAR_t-7) >= 3)
[[t == 10], [t == 4], [t < 4], [10 < t]]
var('x') f(x) = 2/(x^4 + 1) + 3/x show(diff(f(x), x)) 
       
var('x, y') f(x, y)=y^3-x*y^2+cos(x*y)-2 implicit_plot(f(x, y), (x, -10, 10), (y, -10, 10)) 
       
integral(x^2/sqrt(9-x^2), x, 1, 2) 
       
-sqrt(5) + sqrt(2) + 9/2*arcsin(2/3) - 9/2*arcsin(1/3)
-sqrt(5) + sqrt(2) + 9/2*arcsin(2/3) - 9/2*arcsin(1/3)