taylor (f) f;
taylor (f, n, x, a) n = ;
taylor (f, n) (n - 1) f;
taylor (f, a) f .
>>x = sym('x'); >>taylor(sin(x)) ans = x 1/6*x^3 + 1/120*x^5 >>taylor(int(sin(x)) ans = - 1 +1/2*x^2 1/24*x^4 >> |
factor(S). S , - . :
>> x=sym(''); >>factor(x^7-l) ans = ( 1)*(^6 + ^5 + ^4 + ^3 + ^2 + + 1) >>factor(^2 - 1) ans = 2 - 1 >>factor(sym('123456789')) ans = (3)^2*(3803)*(3607) >> |
8. collect()
co11ect(S,v) S v.
9. simple()
simple(S) S , . [R, HOW] = simple(S) .
10. numden
[N,D] = numden(A) . N D .
>> [n,d] = numden(sym(8/10)) n = d = >> syms x y >> [ n, d ] = numden (x*y + y / x) n = y*(x^2 + 1) d = x >> |
symsum
symsum:
symsum(S) - , findsym;
symsum(S, v) - v;
symsum(S, a, b) symsum(S, v, a, b) - b.
3.3-1.
3.3-1. |
>> x = sym(x); >> symsum(x^2) ans = 1/3*x^3-1/2*x^2+1/6*x >>symsum([x, x^2, x^3], 1, 5) ans = [ 15, 55, 225] >> |
, L f(x) , , ( → ), L. : lim f(x) = L.
, .
(, x=a), x=a, x → a 0 x→ a + 0, 0 . x=a, . , x=a.
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f(x) limit(), :
limit(f, x, a) f → ;
limit(f, a) , findsym();
limit(f) - a=0;
limit(f, x, a, `right`) limit(f, x, a, `left`) .
3.3-2.
3.3-2. |
>> syms a x >> limit(sin(a*x)/(a*x)) ans = >> limit(sin(a*x)/x) ans = a >> limit(2*sin(x)/x) ans = >> limit(2+sin(x)/x,0) ans = >> limit(tan(x),pi) ans = >> limit(tan(x),pi/2) ans = NaN >> limit(tan(x),x,pi/2,'right') ans = -Inf >> limit(tan(x),x,pi/2,'left') ans = Inf >> |
3.3-3. y=x2 x=2.
.
3.3-3 |
>> sym x; >> f=sym('x^3'); >> limit(f,x,2,'left') ans = >> |